The existence and asymptotic stability of periodic solutions with an interior layer of Burgers type equations with modular advection

DOI10.1051/mmnp/2019009zbMath1447.35030OpenAlexW2927691157MaRDI QIDQ5229654

Nikolai N. Nefedov

Publication date: 16 August 2019

Published in: Mathematical Modelling of Natural Phenomena (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1051/mmnp/2019009

zbMATH Keywords

lower and upper solutionsexponential asymptotic stability

Mathematics Subject Classification ID

Stability in context of PDEs (35B35) Periodic solutions to PDEs (35B10) Singular perturbations in context of PDEs (35B25) Initial-boundary value problems for second-order parabolic equations (35K20) Semilinear parabolic equations (35K58)

Related Items (7)

Asymptotic solution of the inverse problem for restoring the modular type source in Burgers' equation with modular advection ⋮ Asymptotically stable stationary solutions of the reaction-diffusion-advection equation with discontinuous reaction and advection terms ⋮ Asymptotics of the solution to a stationary piecewise-smooth reaction-diffusion-advection equation ⋮ Internal layer for a singularly perturbed equation with discontinuous right-hand side ⋮ Periodic boundary layer solutions of a reaction-diffusion problem with singularly perturbed boundary conditions of the third kind ⋮ Development of methods of asymptotic analysis of transition layers in reaction-diffusion-advection equations: theory and applications ⋮ Asymptotic solution of the boundary control problem for a Burgers-type equation with modular advection and linear gain

Cites Work

• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Equation admitting linearization and describing waves in dissipative media with modular, quadratic, and quadratically cubic nonlinearities
• On front motion in a Burgers-type equation with quadratic and modular nonlinearity and nonlinear amplification
• Method of upper and lower solutions for parabolic-type equations with discontinuous nonlinearities
• 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
• On the exact and numerical solution of the time-delayed Burgers equation
• On the periodic solution of the Burgers equation: a unified approach
• Approximate solution of the damped Burgers equation
• The solution with internal transition layer of the reaction‐diffusion equation in case of discontinuous reactive and diffusive terms
• On a quasi-linear parabolic equation occurring in aerodynamics
• An asymptotic method of differential inequalities for the investigation of periodic contrast structures: Existence, asymptotics, and stability

This page was built for publication: The existence and asymptotic stability of periodic solutions with an interior layer of Burgers type equations with modular advection