Existence and stability of periodic contrast structures in the reaction-advection-diffusion problem

DOI10.1134/S1061920815020089zbMath1325.35102MaRDI QIDQ2516039

E. I. Nikulin, Nikolai N. Nefedov

Publication date: 10 August 2015

Published in: Russian Journal of Mathematical Physics (Search for Journal in Brave)

Mathematics Subject Classification ID

PDEs in connection with fluid mechanics (35Q35) 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) Existence problems for PDEs: global existence, local existence, non-existence (35A01) Semilinear parabolic equations (35K58)

Related Items (15)

On a New Type of Periodic Fronts in Burgers Type Equations with Modular Advection ⋮ Existence and asymptotic stability of periodic solutions of the reaction-diffusion equations in the case of a rapid reaction ⋮ Asymptotic analysis for the singularly perturbed initial value problem with degenerate equation having triple root ⋮ Existence and stability of periodic contrast structures in the reaction-advection-diffusion problem in the case of a balanced nonlinearity ⋮ Asymptotically stable stationary solutions of the reaction-diffusion-advection equation with discontinuous reaction and advection terms ⋮ 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 ⋮ Burgers-Type Equations with Nonlinear Amplification: Front Motion and Blow-Up ⋮ Asymptotically stable periodic solutions in one problem of atmospheric diffusion of impurities: asymptotics, existence, and uniqueness ⋮ On a periodic inner layer in the reaction-diffusion problem with a modular cubic source ⋮ Existence and asymptotic stability of periodic two-dimensional contrast structures in the problem with weak linear advection ⋮ The existence and asymptotic stability of periodic solutions with an interior layer of Burgers type equations with modular advection ⋮ Development of methods of asymptotic analysis of transition layers in reaction-diffusion-advection equations: theory and applications ⋮ Use of Asymptotics for New Dynamic Adapted Mesh Construction for Periodic Solutions with an Interior Layer of Reaction-Diffusion-Advection Equations

Cites Work

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• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• 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
• Comparison Principle for Reaction-Diffusion-Advection Problems with Boundary and Internal Layers
• Front motion in the parabolic reaction-diffusion problem
• An asymptotic method of differential inequalities for the investigation of periodic contrast structures: Existence, asymptotics, and stability

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