Existence and stability of the solution to a system of two nonlinear diffusion equations in a medium with discontinuous characteristics

DOI10.1134/S0965542521110130OpenAlexW4200110304MaRDI QIDQ2059552

B. V. Tishchenko, N. T. Levashova

Publication date: 14 December 2021

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

Full work available at URL: https://doi.org/10.1134/s0965542521110130

zbMATH Keywords

small parametersystem of nonlinear equationsupper and lower solutionsasymptotics of solutionasymptotic Lyapunov stabilityinner layers

Mathematics Subject Classification ID

Singular perturbations in context of PDEs (35B25) Semilinear parabolic equations (35K58) Initial-boundary value problems for second-order parabolic systems (35K51)

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Cites Work

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• Extremal solutions for nonvariational quasilinear elliptic systems via expanding trapping regions
• Parameter-uniform numerical methods for some linear and nonlinear singularly perturbed convection diffusion boundary turning point problems
• The approach of solutions of nonlinear diffusion equations to travelling front solutions
• Dichotomies in stability theory
• On one model problem for the reaction-diffusion-advection equation
• Asymptotic analysis of solving an inverse boundary value problem for a nonlinear singularly perturbed time-periodic reaction-diffusion-advection equation
• Solving of the coefficient inverse problem for a nonlinear singularly perturbed two-dimensional reaction-diffusion equation with the location of moving front data
• On a periodic inner layer in the reaction-diffusion problem with a modular cubic source
• Existence and stability of a front-type periodic solution of a two-component system of parabolic equations
• Asymptotic stability of a stationary solution of a multidimensional reaction-diffusion equation with a discontinuous source
• The higher integrability of weak solutions of porous medium systems
• Steplike contrast structure in a singularly perturbed system of equations with different powers of small parameter
• Exponential Dichotomies for Almost Periodic Equations
• The solution with internal transition layer of the reaction‐diffusion equation in case of discontinuous reactive and diffusive terms
• A steplike contrast structure in a singularly perturbed system of elliptic equations
• A steplike contrast structure in a singularly perturbed system of elliptic equations with different power of a small parameter