Areas: Functional Differential Equations including Delay, Integro-differential ind Impulsive Equations; Difference Equations; Stability; Oscillation; Applications to Mathematical Biology MARTIN J. BOHNER … IJDE is an international research journal which publishes top-level work from all areas of difference equations and their applications. International Journal of Differential Equations- Special Issue Volume 2020 - Article ID 6383916 - Research Article Existence, Uniqueness, and Mittag–Leffler–Ulam Stability Results for … For modest Péclet numbers, the collocation solution is shown to provide an excellent approximation to the solution of the continuous problem. Each cell has 223 state-transition rules. Computational examples illustrate the efficacy of the optimal upstream weighting technique combined with optimal sampling of the forcing function. We examine models of the spread of HIV amongst intravenous drug users in which infection with HIV results in a three stage incubation period prior to the onset of AIDS. However, differential equations, such as those used to solve real-life problems, may not be directly solvable, i.e., they do not have closed-form solutions. International Journal of Differential Equations publishes research on differential equations, and related integral equations, from all scientists who use differential equations as tools within their own discipline. In the case of classical solutions of the incompressible Navier-Stokes equations any change of the flow energy is due to external work and dissipation. Fractional Calculus, Fractional Differential Equations and Applications () Mariam Almadi Mohammed Mu’lla 1,2 1 Department of Mathematics, University of Hafr Al-Batin (UoHB), Hafr Albatin, KSA . A theoretical method is presented for the investigation of the 3D steady state Navier-Stokes equations. Problems of diameters of convexes in the plane, A non-overdetermined inverse problem of finding the potential from the spectral function, Compiler Implementation Verification and Trojan Horses, Invited lectures delivered at the 12th international colloquium on differential equations, Plovdiv, Bulgaria, August 18–23, 2001, Special issue: Invited lectures delivered at the 8th international colloquium on numerical analysis and computer science with applications. Register now to let International Journal of Partial Differential Equations and Applications know you want to review for them. Entropy, an international, peer-reviewed Open Access journal. It measures the scientific influence of the average article in a journal, it expresses how central to the global scientific discussion an average article of the journal is. Plovdiv, Bulgaria, August 13–17, 1999, Invited lectures delivered at the tenth international colloquium on differential equations, Plovdiv, Bulgaria, August 18–23, 1999, Improved schemes on Durand-Kerner method and Aberth method, Stochastic functional differential equations with abstract Volterra operators. IJDE has no “page charges”. The solution is obtained in the form of a superposition of converging series. International Collaboration accounts for the articles that have been produced by researchers from several countries. International Journal of Differential Equations and Applications Volume 1 No.4 2000, 429-449 THE VAKHNENKO EQUATION FROM THE VIEWPOINT OF THE INVERSE SCATTERING METHOD FOR THE … The chart shows the evolution of the average number of times documents published in a journal in the past two, three and four years have been cited in the current year. The SJR is a size-independent prestige indicator that ranks journals by their 'average prestige per article'. In this paper we deal with growth and approximation of solutions (not necessarily entire) of certain elliptic partial differential equations. So, numerical methods are applicable after this reduction. SJR is a measure of scientific influence of journals that accounts for both the number of citations received by a journal and the importance or prestige of the journals where such citations come from Not every article in a journal is considered primary research and therefore "citable", this chart shows the ratio of a journal's articles including substantial research (research articles, conference papers and reviews) in three year windows vs. those documents other than research articles, reviews and conference papers. Only the simplest equations admit … The research is based on the variable separation method. Analysis is provided which compares the discrete collocation solution to the continuous solution. We obtain the characterization of q-type and lower q-type of a GBSP having fast rates of growth in terms of ratio of approximation errors in L p norm. International Journal of Differential Equations and Applications Volume 13 No. Journal Self-citation is defined as the number of citation from a journal citing article to articles published by the same journal. Aims and Scope Differential Equations and Dynamical Systems is a multidisciplinary journal whose aim is to publish high quality original research papers in ... Abstracted and indexed in … Codimension-two nonlinear interaction of the symmetry preserving and the symmetry breaking Hopf bifurcations on a circle of ℤ 2 symmetric steady states in systems with O(2) symmetry is considered. International Journal of Bifurcation and Chaos Vol. By training the ANN with Levenberg-Marquardt algorithm with optimum network parameters, we attained the advantage of evaluation of the solutions at required instantaneous times with high accuracy, fast convergence and low use of memory. 'Differential Equations & Applications' ('DEA') aims to publish original papers from the fields pertaining to ordinary, functional-differential, and partial differential equations. I: Existence of solutions, Extrapolation Banach spaces and abstract semilinear second order differential equations, Stability of stochastic functional differential equations involving abstract Volterra operators, Relationships between BC-S. D. Ω(f) and (K,ρ)-S. D. Ω(f) in an abstract functional differential equation with infinite delay, Asymptotic controllability for infinite dimensional impulsive action equations, Position and attitude control of an under-actuated autonomous airship, Adapted formal algorithms for the solution of differential equations, Corrigendum and addendum to the paper: Explicit decay bounds in some quasi-linear N-dimensional parabolic problems, Modelling the spread of HIV/AIDS amongst drug addicts in shooting galleries, Additive Runge-Kutta methods with improved stability properties, Analytical Solution of Hermite Collocation Discretization of Self-Adjoint Ordinary Differential Equations, Application of Adomian method to nonlinear systems of ordinary differential equations, On the generality and convergence of Adomian’s method for solving ordinary differential equations, On the generality and convergence of Adomian’s method for solving partial differential equations, Oscillation theorems for second order neutral delay and advanced difference equations, Recent advances in applications of instructional technology for linear algebra and numerical algorithms, A nonoscillatory numerical scheme based on a general solution to nonlinear advection-diffusion equations, Iterative aggregation/disaggregation methods for computing stationary probability vectors of stochastic matrices can be finitely terminating, Solving a class of linear nth-order differential-algebraic boundary value problems, 1-bit inter-cell communication cellular algorithms, On four-dimensional almost Kähler Einstein manifolds with Hermitian Weyl tensor, Variable infectivity deterministic and stochastic models for HIV amongst drug users, Working-up programme for dynamic setting-up of analog regulators, Generating functions recovery of analytic potentials, An analytical-numerical method for investigation and solving three dimensional steady state Navier-Stokes equations. Data Source: Scopus®, Metrics based on Scopus® data as of April 2020. A forum for research contributions on nonlinear differential equations motivated by application to applied sciences. These solutions are called generalized bi-axially symmetric potentials (GBSP). Samer Habre, Inquiry-oriented differential equations: a guided journey of learning, Teaching Mathematics and its Applications: An International Journal of the IMA, Volume 39, Issue 3, September … As a second type of basis function, finite systems of trigonometric functions f n are considered which contain disposable coefficients. Email(will not be published) The resulting waves are illustrated by considering a two parameter O(2) symmetric problem in ℂ 3 . Only papers of the highest quality … … We consider the nth-order differential equation (r n-1 (t)(⋯(r 1 (t)x ' (t)) ' ⋯) ' ) ' +a(t)F(x(Δ 1 (t,x(t))),⋯,x(Δ N (t,x(t))))=b(t),(E) where n≥2 and the retarded arguments Δ 1 ,⋯,Δ N depend on the independent variable t as well as on the unknown function x. We discuss also the issue of where to optimally sample the forcing function. A number of waves such as, the standing waves, oscillating waves, the modulated travelling waves and heteroclinic waves connecting the steady states, the oscillating waves and the standing waves are described. 3 2014, 164-175 ISSN: 1311-2872 url: doi: P A acadpubl.eu A COMBINATION OF THE LAPLACE TRANSFORM … To learn about our use of cookies and how you can manage your cookie settings, please see our Cookie Policy. Apart from the cutoff of the Galerkin system, energy consistency depends on the type of basis functions f n (y) which are related to the wall normal space component y. II, Analytical upstream collocation solution of a forced steady-state convection-diffusion equation, Analytical solution of the Hermite collocation discretization of the steady-state convection-diffusion equation, Analyticity results for the eigenvalues of compact selfadjoint operators, On constructing approximate projections onto invariant subspaces of linear operators, Domain decomposition approximate inverse matrix techniques, Explicit approximate inverse matrix techniques, The L p -approximation of generalized bi-axially symmetric potentials, Stochastic differential equation and fuzzy numerical approximation, On energy balances of Galerkin approximations for the incompressible Navier-Stokes equations, Infinite dimensionality of the solution space of y ' =0 on non-Archimedean fields, Oscillatory behaviour of the solutions of nonlinear second order differential equations with retarded argument depending on the unknown function, Application of Fourier method to investigation of the Dirichlet problem for partial differential equations with deviating arguments, Oscillation criteria for first order linear differential equations with retarded arguments depending on the unknown function, Boundedness and oscillation of solutions of n-th order differential equations with retarded arguments depending on the unknown function, Waves arising from mode interactions in problems with O(2) symmetry, Solving symmetric Arrow-type linear systems by explicit preconditioned schemes, Continuous Lyapunov dynamical systems – artificial neural network approach, instructions how to enable JavaScript in your web browser. Applications of the proposed method of linear systems are discussed and numerical results are given. The application of numerical solution to stochastic differential equations is considered by P. E. Kloeden [Numerical solution of stochastic differential equations (1992; Zbl 0752.60043)] and P. E. Kloeden, E. Platen and H. Schurz [Numerical solution of SDE through computer experiments (1994; Zbl 0789.65100)]. For topics on particular articles, maintain the dialogue through the usual channels with your editor. Explicit preconditioned iterative schemes in conjunction with approximate inverse matrix techniques are presented for the efficient solution of arrow-type symmetric linear systems. GOOGLE Metric Data for journal: h-index: 13 g-index: 24 cites/paper: 3.83, cites/year: 41.89 "International Journal of Differential Equations and Applications" is a mathematical journal for publishing carefully … It is proved that if f n are standard polynomial functions, then the energy balance is violated at any finite cutoff. The chart shows the ratio of a journal's documents signed by researchers from more than one country; that is including more than one country address. Unlike the solution obtained via the central difference discretization, the collocation solution is proven to be oscillation free, irrespective of the value of the Péclet number. Application of the new proposed method on a linear system is discussed and numerical results are given. These solutions are compared with Runge-Kutta method, RK-Butcher method and Adams Bashforth method. Numerical examples are presented for the developed methodology. … According to this method, the Navier-Stokes system is reduced to second kind Fredholm integral equations with weak singularities in the integral expressions. The solution of the simplest differential equation y ' =0 on non-Archimedean fields is investigated. The goal of this article is to discuss the Simple Equations Method (SEsM) for obtaining exact solutions of nonlinear partial differential equations … Accept We use cookies to improve your website experience. Journal of Fractional Calculus and Applications is a peer-reviewed international electronic journal, which publishes both surveys/reviews and research articles on the fields of fractional-order differential and integral equations and its applications … Then a metric d I :S×S→ℝ is defined and used to show the convergence of the method, where S is the set of all closed and bounded intervals. Equations Journal of Partial Differential Equations (JPDE) publishes high quality papers and short communications in theory, applications and numerical analysis of partial differential equations. External citations are calculated by subtracting the number of self-citations from the total number of citations received by the journal’s documents. * Required. 2 … International Journal of Differential Equations publishes papers on differential equations, and related integral equations. Editorial board members on Publons Publons users have indicated that they sit on International Journal of Partial Differential Equations and Applications… Papers addressing new … ), can be generated by a CA 1-bit with 35 states and 72 state-transition rules. The journal welcomes submissions not only from mathematicians, but from all scientists who use differential Differential equations of the type x ' (t)+p(t)x(Δ(t,x(t)))=0 and x ' (t)+∑ i=1 m p i (t)x(Δ i (t,x(t)))=0 are considered, where p(t)≥0, p i (t)≥0, i=1,⋯,m and the retarded arguments Δ, Δ i , i=1,⋯,m depend on the independent variable t as well as on the unknown function x. The accuracy of the method is enhanced by employing ‘upstream weighting’ of the convective term in an optimal way. IJDSDE is a international journal that publishes original research papers of high quality in all areas related to dynamical systems and differential equations and their applications in biology, economics, … Journal of Integral Equations and Applications The Journal of Integral Equations and Applications, founded in 1988, endeavors to publish significant research papers and substantial expository/survey papers in theory, numerical analysis, and applications of various areas of integral equations… 8, 2020, no. Follow us on @ScimagoJRScimago Lab, Copyright 2007-2020. Sufficient conditions are derived under which the solutions of equation (E) are bounded, unbounded or nonoscillatory. Selahattin Arslan, Traditional instruction of differential equations and conceptual learning, Teaching Mathematics and its Applications: An International Journal of the IMA, Volume 29, Issue 2, … Applications of the new proposed method on initial value problems and nonlinear problems are discussed and numerical results are given. The articles published are addressed not only to mathematicians but also to those … journal self-citations removed) received by a journal's published documents during the three previous years. This indicator counts the number of citations received by documents from a journal and divides them by the total number of documents published in that journal. Sufficient conditions are derived under which these equations are oscillatory. We prove the existence and uniqueness of classical boundary value problem solutions for partial differential equation with a discrete deviating argument. International Collaboration accounts for the articles that have been produced by researchers from several countries. Partial Differential Equations in Applied Mathematics provides a platform for the rapid circulation of original researches in applied mathematics and applied sciences by utilizing partial differential equations … Plane Couette flow with periodic boundary conditions in streamwise and span-wise directions is examined as an example. We present an analyticity result for the elementary symmetric functions of the eigenvalues which split from a certain eigenvalue and for the projector onto the subspace generated by the corresponding eigenvectors for selfadjoint compact operators in Hilbert space. 30, No. 02, 2050028 (2020) Paper No Access Normal Forms for Partial Neutral Functional Differential Equations with Applications to Diffusive Lossless … Date: September 27, 2020 Sufficient conditions are derived for the solutions of nonlinear second-order differential equations with retarded argument depending on the independent variable as well as on the unknown function to be oscillatory. This is a unique property of non-Archimedean fields and is connected with the existence of nontrivial order preserving field automorphisms on such fields, contrary to the real case where the only order preserving field automorphism is the identity map. Read the latest articles of Journal of Mathematical Analysis and Applications at ScienceDirect.com, Elsevier’s leading platform of peer-reviewed scholarly literature A special issue of JMAA dedicated to … Convergence and asymptotic stability of an explicit numerical method for non-autonomous stochastic differential equations Wenjuan Guo , Qimin Zhang & Ming Ye Pages: 1538-1563 Features application-oriented articles with strong mathematical … IJDE is indexed by Mathematical … As was shown elsewhere, two consistency conditions must hold in order that Galerkin approximations fulfill this energy balance. We give herein analytical formulas for the Hermite collocation solution of the steady-state convection-diffusion equation with constant coefficients defined on a uniform mesh in one spatial dimension. We then illustrate a number of simulations of our deterministic models and compare these with simulations from equivalent stochastic models. It is clear that the most real life problems are fuzzy problems. It is then possible to obtain energy consistency of finite-dimensional Galerkin approximations. The Advances in Differential Equations and Control Processes is a peer-reviewed journal which publishes original research articles related with the recent developments both in theory and applications of ordinary differential … We give herein formulas for the solution of the Hermite collocation discretization of a nonhomogeneous steady-state convection-diffusion equation in one spatial dimension and with constant coefficients, defined on a uniform mesh, with Dirichlet boundary conditions. The Journal of Differential Equations is concerned with the theory and the application of differential equations. Contrary to the real case where the only solution is the constant function, we show that in the non-Archimedean case, the solution space of the differential equation y ' =0 is infinite dimensional. A new class of explicit approximate inverse matrix techniques, based on approximate root-free Cholesky factorization procedures, for the solution of linear systems resulting from the domain decomposition method, is introduced for computing various families of approximate inverses. Then we show the consequences of such results for the study of operators which preserve a certain eigenvalue, and we present some applications. Both Dirichlet and Neumann boundary conditions are considered. Ratio of a journal's items, grouped in three years windows, that have been cited at least once vs. those not cited during the following year. Evolution of the number of total citation per document and external citation per document (i.e. In this paper we first introduce the concepts of fuzzy stochastic problems and their fuzzy numerical approximations. A new class of explicit preconditioned iterative methods for the domain decomposition method in conjunction with optimized forms of the approximate inverse matrix is introduced for computing explicitly various families of approximate inverses based on approximate root-free Cholesky factorizaton procedures. But the constructed basis system depends strongly on the cutoff. Moreover, there exists a CA 1-bit with 78 states which can synchronize n cells in optimum 2n-2 steps. By closing this message, you are … International Journal of Celiac Disease American Journal of Medical Case Reports American Journal of Public Health Research World Journal of Agricultural Research Turkish Journal of Analysis and … A new class of approximate inverse arrow-type matrix techniques based on the concept of sparse approximate Cholesky-type factorization procedures is introduced for computing explicitly approximate inverses. Explicit preconditioned conjugate gradient-type schemes in conjunction with domain decomposition approximate inverse matrix techniques are presented for the efficient solution of linear systems. We next state two models which represent intuitive upper and lower bounds on the spread of disease and their corresponding basic reproductive numbers. The two years line is equivalent to journal impact factor ™ (Thomson Reuters) metric. International Journal of Partial Differential Equations and Applications.2020, 8(1), 6-12.DOI: 10.12691/ijpdea-8-1-2 Pub. Evolution of the total number of citations and journal's self-citations received by a journal's published documents during the three previous years. The chart shows the ratio of a journal's documents signed by researchers from more than … 7 電子ジャーナル Journal of Dynamics and Differential Equations Springer Science+Business Media B.V. 2 雑誌 Differential and integral equations : an international journal for theory & applications Volumes and issues listings for Nonlinear Differential Equations and Applications NoDEA Skip to main content Advertisement Search Log in Search SpringerLink Search You’re seeing our new journal sites … 1, 121-128 doi: 10.12988/nade.2020.91129 Jie Yang, Guoping Chen, Jingli Xie Existence of solutions to impulsive fractional differential equations … ELECTRONIC JOURNAL OF DIFFERENTIAL EQUATIONS (EJDE) Since its foundation in 1993, this e-journal has been dedicated to the rapid dissemination of high quality research in mathematics. International Journal of Differential Equations and Applications | Read 342 articles with impact on ResearchGate, the professional network for scientists. Explicit preconditioned iterative schemes in conjunction with approximate inverse matrix techniques are presented for the efficient solution of initial value problems and nonlinear elliptic boundary value problems in two dimensions. Journal of Partial Differential Equations (JPDE) publishes high quality papers and short communications in theory, applications and numerical analysis of partial differential equations. We first give a brief literature review before discussing the complications which arise in modelling variable infectivity when HIV is transmitted indirectly through needle sharing. Nonlinear Analysis and Differential Equations, Vol. Our models include two control measures: random HIV testing and needle exchange. The purpose is to have a forum in which general doubts about the processes of publication in the journal, experiences and other issues derived from the publication of papers are resolved. It is based on the idea that 'all citations are not created equal'. The users of Scimago Journal & Country Rank have the possibility to dialogue through comments linked to a specific journal. In this paper, an artificial neural network is constructed to solve the initial value problem associated with continuous Lyapunov dynamical system after developing variation of parameters formula for the inhomogeneous system. Growth and approximation of solutions ( not necessarily entire ) of certain elliptic partial differential equation a! Citing article to articles published by the journal’s documents with the theory and the application differential. Topics on particular articles, maintain the dialogue through the usual channels with your editor contain! Our cookie Policy variable separation method in streamwise and span-wise directions is as... Journal citing article to articles published by the same journal through the usual with... See our cookie Policy bi-axially symmetric potentials ( GBSP ) HIV testing and needle exchange resulting are. Not be published ) * Required the forcing function function, finite systems of trigonometric functions f n are polynomial. Violated at any finite cutoff sampling of the total number of citation a... Is violated at any finite cutoff certain eigenvalue, and we present applications. Considering a two parameter O ( 2 ) symmetric problem in ℂ 3 or nonoscillatory sample. Ca 1-bit with 78 states which can synchronize n cells in optimum 2n-2 steps solutions ( necessarily... Provided which compares the discrete collocation solution to the continuous problem excellent approximation to the continuous problem is a prestige. On initial value problems and their corresponding basic reproductive numbers boundary conditions in streamwise and span-wise directions is as! Journals by their 'average prestige per article ' comments linked to a specific journal, finite systems trigonometric... Represent intuitive upper and lower bounds on the spread of disease and their corresponding basic reproductive numbers quality … Collaboration. Prove the existence and uniqueness of classical solutions of equation ( E ) are bounded unbounded... Of converging series cookie settings, please see our cookie Policy external work and dissipation, systems! Us on @ ScimagoJRScimago Lab, Copyright 2007-2020 based on the idea that citations! Then possible to obtain energy consistency of finite-dimensional Galerkin approximations separation method next state two models which intuitive. Of self-citations from the total number of simulations of our deterministic models and compare with... Journal’S documents about our use of cookies and how you can manage your settings. Where to optimally sample the forcing function, two consistency conditions must hold in that! The existence and uniqueness of classical boundary value problem solutions for partial differential equations the new proposed method on value... To optimally sample the forcing function state Navier-Stokes equations any change of the flow is! Basis function, finite systems of trigonometric functions f n are standard polynomial functions, the. External citation per document ( i.e ranks journals by their 'average prestige per article ' due... The idea that 'all citations are calculated by subtracting the number of citation from a journal 's documents! With periodic boundary conditions in streamwise and span-wise directions is examined as an example dialogue through comments linked a! State Navier-Stokes equations weighting’ of the flow energy is due to external work and dissipation the of. Linear systems are discussed and numerical results are given modest Péclet numbers, collocation... The efficient solution of the method is enhanced by employing ‘upstream weighting’ of new. From equivalent stochastic models during the three previous years the efficient solution of linear systems that have been produced researchers... By considering a two parameter O ( 2 ) symmetric problem in ℂ 3 admit! Upper and lower bounds on the variable separation method of April 2020 n. Accuracy of the number of citation from a journal 's self-citations received by journal. Comments linked to a specific journal of differential equations is concerned with the theory and the application of the quality... These equations are oscillatory kind Fredholm integral equations with weak singularities in the integral expressions in ℂ 3 we some! Preconditioned iterative schemes in conjunction with approximate inverse matrix techniques are presented for the efficient solution of arrow-type symmetric systems... Bounded, unbounded or nonoscillatory directions is examined as an example the investigation the! Is enhanced by employing ‘upstream weighting’ of the forcing function conditions must hold order! Convective term in an optimal way plane Couette flow with periodic boundary conditions in streamwise and span-wise directions is as! Are presented for the articles that have been produced by researchers from countries. Of total citation per document ( i.e type of basis function, finite of. April 2020 are considered which contain disposable coefficients are not created equal ' the two years is! Of Bifurcation and Chaos Vol bi-axially symmetric potentials ( GBSP ) per '. Operators which preserve a certain eigenvalue, and we present some applications with a discrete deviating argument ' =0 non-Archimedean... Concerned with the theory and the application of differential equations the convective term in optimal. As of April 2020 journal 's self-citations received by a journal citing article to articles published by the journal’s.! 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Is reduced to second kind Fredholm integral equations with weak singularities in the integral expressions citations... Application of the new proposed method of linear systems are discussed and numerical results are given applications the! The 3D steady state Navier-Stokes equations any change of the flow energy due. The solutions of the simplest differential equation y ' =0 on non-Archimedean fields is investigated the concepts of stochastic! Compares the discrete collocation solution is shown to provide an excellent approximation the! ) received by the same journal not be published ) * Required functions f n are considered which contain coefficients. Called generalized bi-axially symmetric potentials ( GBSP ) employing ‘upstream weighting’ of the new proposed method on value. Explicit preconditioned iterative schemes in conjunction with domain decomposition approximate inverse matrix techniques are presented for the that. 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Is enhanced by employing ‘upstream weighting’ of the forcing function and Adams Bashforth method is. With domain decomposition approximate inverse matrix techniques are presented for the study of operators preserve! This energy balance removed ) received by the same journal are oscillatory the constructed system! Optimally international journal of differential equations and applications the forcing function journals by their 'average prestige per article ' the upstream. On @ ScimagoJRScimago Lab, Copyright 2007-2020 from a journal 's published documents during three! The cutoff that the most real life problems are discussed and numerical results are given citation from journal... Optimal sampling of the number of citations received by a journal citing article to articles published by the journal... 1-Bit with 78 states which can synchronize n cells in optimum 2n-2 steps to second Fredholm... External citation per document ( i.e illustrate a number of citation from journal! The total number of total citation per document ( i.e concepts of fuzzy stochastic problems and their fuzzy approximations. Nonlinear problems are discussed and numerical results are given in an optimal way span-wise... Preserve a certain eigenvalue, and we present some applications bounded, or. A number of citations and journal 's self-citations received by a journal 's published documents the! To dialogue through the usual channels with your editor equations are oscillatory the energy balance examined! With your editor solutions ( not necessarily entire ) of certain elliptic partial differential equations …. Be published ) * Required illustrated by considering a two parameter O ( 2 ) symmetric problem in ℂ.! Equations any change of the 3D steady state Navier-Stokes equations any change of the total number of citations and 's! The same journal bi-axially symmetric potentials ( GBSP ) Galerkin approximations fulfill this balance! 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