Results 11 to 20 of about 93 (92)
Oscillatory and periodic solutions to a diffusion equation of neutral type
International Journal of Mathematics and Mathematical Sciences, Volume 22, Issue 2, Page 313-348, 1999., 1999 We examine a PDE with piecewise constant time delay. The equation is of neutral type since it contains the derivative ut at different values of the t‐argument. Furthermore, the argument deviation changes its sign within intervals of unit length, so that the given PDE is alternately of retarded and advanced type.
Joseph Wiener, William Heller
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Boundary layer analysis for a 2-D Keller-Segel model
Open Mathematics, 2020 We study the boundary layer problem of a Keller-Segel model in a domain of two space dimensions with vanishing chemical diffusion coefficient. By using the method of matched asymptotic expansions of singular perturbation theory, we construct an accurate ...
Meng Linlin, Xu Wen-Qing, Wang Shu
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Singularly perturbed telegraph equations with applications in the random walk theory
International Journal of Stochastic Analysis, Volume 11, Issue 1, Page 9-28, 1998., 1997 In the paper we analyze singularly perturbed telegraph systems applying the newly developed compressed asymptotic method and show that the diffusion equation is an asymptotic limit of singularly perturbed telegraph system of equations. The results are applied to the random walk theory for which the relationship between correlated and uncorrelated ...
Jacek Banasiak, Janusz R. Mika
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Open Mathematics, 2018 The main purpose of this paper is to study the initial layer problem and the infinite Prandtl number limit of Rayleigh-Bénard convection with an ill prepared initial data.
Fan Xiaoting +3 more
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Relative entropy in diffusive relaxation [PDF]
, 2012 We establish convergence in the diffusive limit from entropy weak solutions of the equations of compressible gas dynamics with friction to the porous media equation away from vacuum.
Tzavaras, Athanasios E. +1 more
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Boundary value problems for the diffusion equation with piecewise continuous time delay
International Journal of Mathematics and Mathematical Sciences, Volume 20, Issue 1, Page 187-195, 1997., 1996 A study is made of partial differential equations with piecewise constant arguments. Boundary value problems for three types of equations are discussed delayed; alternately of advanced and retarded type; and most importantly, an equation of neutral type (that is, including the derivative at different values of time t).
Joseph Wiener, Lokenath Debnath
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Advanced Nonlinear Studies, 2019 This paper studies a singular perturbation result for a class of generalized diffusive logistic equations, dℒu=uh(u,x){d\mathcal{L}u=uh(u,x)}, under non-classical mixed boundary conditions, ℬu=0{\mathcal{B}u=0} on ∂Ω{\partial\Omega}.
Fernández-Rincón Sergio +1 more
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A survey of partial differential equations with piecewise continuous arguments
International Journal of Mathematics and Mathematical Sciences, Volume 18, Issue 2, Page 209-228, 1995., 1995 Some work is described and new topics are posed on initial and boundary‐value problems for partial differential equations whose arguments have intervals of constancy. These equations are of considerable theoretical and applied interest.
Joseph Wiener, Lokenath Debnath
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Choquard-type equations with Hardy–Littlewood–Sobolev upper-critical growth
Advances in Nonlinear Analysis, 2018 We are concerned with the existence of ground states and qualitative properties of solutions for a class of nonlocal Schrödinger equations. We consider the case in which the nonlinearity exhibits critical growth in the sense of the Hardy–Littlewood ...
Cassani Daniele, Zhang Jianjun
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A parabolic differential equation with unbounded piecewise constant delay
International Journal of Mathematics and Mathematical Sciences, Volume 15, Issue 2, Page 339-346, 1992., 1991 A partial differential equation with the argument [λt] is studied, where [•] denotes the greatest integer function. The infinite delay t − [λt] leads to difference equations of unbounded order.
Joseph Wiener, Lokenath Debnath
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