Existence and stability of periodic contrast structures in the reaction-advection-diffusion problem in the case of a balanced nonlinearity

DOI10.1134/S0012266117040103zbMath1372.35022MaRDI QIDQ2399393

E. I. Nikulin, Nikolai N. Nefedov

Publication date: 23 August 2017

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

zbMATH Keywords

asymptotic method of differential inequalitiesinternal transition layersmall advection

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) Asymptotic expansions of solutions to PDEs (35C20) Semilinear parabolic equations (35K58)

Related Items (10)

Contrast structures in the reaction-diffusion-advection problem in the case of a weak reaction discontinuity ⋮ Existence and asymptotic stability of periodic solutions of the reaction-diffusion equations in the case of a rapid reaction ⋮ Existence and asymptotic stability of a stationary boundary-layer solution of the two-dimensional reaction-diffusion-advection problem ⋮ Existence and stability of solutions with internal transition layer for the reaction-diffusion-advection equation with a KPZ-nonlinearity ⋮ On the existence and asymptotic stability of periodic contrast structures in quasilinear reaction-advection-diffusion equations ⋮ Contrast structures in the reaction-advection-diffusion problem appearing in a drift-diffusion model of a semiconductor in the case of nonsmooth reaction ⋮ On a periodic inner layer in the reaction-diffusion problem with a modular cubic source ⋮ Existence of a solution in the form of a moving front of a reaction-diffusion-advection problem in the case of balanced advection ⋮ Solution with an inner transition layer of a two-dimensional boundary value reaction-diffusion-advection problem with discontinuous reaction and advection terms ⋮ Development of methods of asymptotic analysis of transition layers in reaction-diffusion-advection equations: theory and applications

Cites Work

• Singularly perturbed problems with boundary and internal layers
• Periodic solutions with boundary layers of a singularly perturbed reaction-diffusion model
• Existence and asymptotic stability of periodic solutions with an interior layer of reaction-advection-diffusion equations
• Existence and stability of periodic contrast structures in the reaction-advection-diffusion problem
• Comparison Principle for Reaction-Diffusion-Advection Problems with Boundary and Internal Layers
• An asymptotic method of differential inequalities for the investigation of periodic contrast structures: Existence, asymptotics, and stability
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