Asymptotic stability of a stationary solution of a multidimensional reaction-diffusion equation with a discontinuous source

DOI10.1134/S0965542519040109zbMath1423.35232OpenAlexW2949225890MaRDI QIDQ2332648

A. O. Orlov, N. T. Levashova, Nikolai N. Nefedov

Publication date: 4 November 2019

Published in: Computational Mathematics and Mathematical Physics (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1134/s0965542519040109

zbMATH Keywords

comparison principlereaction-diffusion problemasymptotics of solutioninternal layersLyapunov asymptotic stability

Mathematics Subject Classification ID

Singular perturbations in context of PDEs (35B25) Reaction-diffusion equations (35K57) Initial-boundary value problems for second-order parabolic equations (35K20) Asymptotic expansions of solutions to PDEs (35C20) Semilinear parabolic equations with Laplacian, bi-Laplacian or poly-Laplacian (35K91) Semilinear elliptic equations with Laplacian, bi-Laplacian or poly-Laplacian (35J91)

Related Items (14)

Contrast structures in the reaction-diffusion-advection problem in the case of a weak reaction discontinuity ⋮ Existence of a periodic solution in the form of a two-dimensional front in a system of parabolic equations ⋮ Asymptotically stable stationary solutions of the reaction-diffusion-advection equation with discontinuous reaction and advection terms ⋮ A class of singularly perturbed equations with discontinuous right-hand side in the critical case ⋮ On unstable contrast structures in one-dimensional reaction-diffusion-advection problems with discontinuous sources ⋮ Asymptotics of the solution to a stationary piecewise-smooth reaction-diffusion-advection equation ⋮ On a periodic inner layer in the reaction-diffusion problem with a modular cubic source ⋮ Internal layer for a singularly perturbed equation with discontinuous right-hand side ⋮ Existence and stability of periodic contrast structure in reaction-advection-diffusion equation with discontinuous reactive and convective terms ⋮ Existence and stability of a front-type periodic solution of a two-component system of parabolic equations ⋮ Existence and stability of the solution to a system of two nonlinear diffusion equations in a medium with discontinuous characteristics ⋮ Solution of contrast structure type for a reaction-diffusion equation with discontinuous reactive term ⋮ Development of methods of asymptotic analysis of transition layers in reaction-diffusion-advection equations: theory and applications ⋮ Existence and stability of periodic solution of contrast structure type in discontinuous singularly perturbed reaction-convection-diffusion problem

Cites Work

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