Existence and asymptotic stability of periodic two-dimensional contrast structures in the problem with weak linear advection

DOI10.1134/S0001434619110105zbMath1435.35033OpenAlexW2998424827WikidataQ126469683 ScholiaQ126469683MaRDI QIDQ2304489

E. I. Nikulin, Nikolai N. Nefedov

Publication date: 12 March 2020

Published in: Mathematical Notes (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1134/s0001434619110105

zbMATH Keywords

internal transition layerreaction-advection-diffusion equationsmethod of differential inequalitiessingularly perturbed parabolic problemperiodic contrast structures

Mathematics Subject Classification ID

Stability in context of PDEs (35B35) 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) Semilinear parabolic equations (35K58)

Related Items (5)

Contrast structures in the reaction-diffusion-advection problem in the case of a weak reaction discontinuity ⋮ Existence and stability of solutions with internal transition layer for the reaction-diffusion-advection equation with a KPZ-nonlinearity ⋮ Multizonal boundary and internal layers in the singularly perturbed problems for a stationary equation of reaction-advection-diffusion type with weak and discontinuous nonlinearity ⋮ Contrast structures in the reaction-advection-diffusion problem appearing in a drift-diffusion model of a semiconductor in the case of nonsmooth reaction ⋮ Development of methods of asymptotic analysis of transition layers in reaction-diffusion-advection equations: theory and applications

Cites Work

• Existence and stability of solutions with boundary layers in multidimensional singularly perturbed reaction-diffusion-advection problems
• Contrast structures in singularly perturbed quasilinear reaction-diffusion-advection equations
• Singularly perturbed problems with boundary and internal layers
• Existence of periodic solutions of semilinear parabolic equations and the method of upper and lower solutions
• Comparison principles for reaction-diffusion systems: Irregular comparison functions and applications to questions of stability and speed of propagation of disturbances
• On a contrast steplike structure for a class of second-order nonlinear singularly perturbed equations
• Existence and asymptotic stability of periodic solutions of the reaction-diffusion equations in the case of a rapid reaction
• Multi-dimensional stationary internal layers for spatially inhomogeneous reaction-diffusion equations with balanced nonlinearity
• 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
• Periodic traveling waves and locating oscillating patterns in multidimensional domains
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