This article is cited in 7 papers

Partial Differential Equations

Asymptotic solution of the boundary control problem for a Burgers-type equation with modular advection and linear gain

V.T. Volkov, N. N. Nefedov

Faculty of Physics, Lomonosov Moscow State University, 119991, Moscow, Russia

Abstract: A singularly perturbed periodic problem for a parabolic reaction–diffusion–advection Burgers-type equation with modular advection and linear gain is considered. Conditions for the existence, uniqueness, and asymptotic Lyapunov stability of a periodic solution with an internal transition layer are obtained, and its asymptotic approximation is constructed. Asymptotic analysis is applied in solving the boundary control problem to achieve the required law of front’s motion. The concept of an asymptotic solution of this problem is formulated, sufficient conditions for the existence and uniqueness of the solution are obtained, and an asymptotic approximation of the solution is constructed.

Key words: singularly perturbed parabolic equations, periodic problems, reaction–diffusion equations, contrast structures, inner layers, fronts, asymptotic, methods, differential inequalities, asymptotic Lyapunov stability, Burgers equations with modular advection, inverse coefficient problem, asymptotic solution of inverse problem.

UDC: 519.956.4

Received: 15.10.2021
Revised: 04.04.2022
Accepted: 08.06.2022

DOI: 10.31857/S0044466922110138

 English version: Computational Mathematics and Mathematical Physics, 2022, 62:11, 1849–1858

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