Solution of contrast structure type for a parabolic reaction-diffusion problem in a medium with discontinuous characteristics

DOI10.1134/S0012266118050105zbMath1395.35014OpenAlexW2806170229MaRDI QIDQ1660881

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

Publication date: 16 August 2018

Published in: Differential Equations (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1134/s0012266118050105

zbMATH Keywords

stable periodic solutiontwo-dimensional domainasymptotic method of differential inequalitiesinternal layer

Mathematics Subject Classification ID

Periodic solutions to PDEs (35B10) Singular perturbations in context of PDEs (35B25) Reaction-diffusion equations (35K57) Initial-boundary value problems for second-order parabolic equations (35K20) PDEs with low regular coefficients and/or low regular data (35R05) Semilinear parabolic equations (35K58)

Related Items (8)

Internal layer for a system of singularly perturbed equations with discontinuous right-hand side ⋮ On a periodic inner layer in the reaction-diffusion problem with a modular cubic source ⋮ 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 ⋮ 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 ⋮ Asymptotic stability of a stationary solution of a multidimensional reaction-diffusion equation with a discontinuous source ⋮ Existence and stability of periodic solution of contrast structure type in discontinuous singularly perturbed reaction-convection-diffusion problem

Cites Work

• Strong solutions of periodic parabolic problems with discontinuous nonlinearities
• Contrast structures in singularly perturbed quasilinear reaction-diffusion-advection equations
• On one model problem for the reaction-diffusion-advection equation
• Contrast structures in multidimensional singularly perturbed reaction-diffusion-advection problems
• Time-independent reaction-diffusion equation with a discontinuous reactive term
• An asymptotic method of differential inequalities for the investigation of periodic contrast structures: Existence, asymptotics, and stability
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