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Abstract <p>The paper considers a boundary-value problem for a singularly perturbed elliptic system of fast and slow equations, commonly referred to as a system of Tikhonov type. A distinctive feature of the problem is the presence of terms containing the squared gradient of the unknown function (KPZ nonlinearities). A boundary layer asymptotic expansion of the solution is constructed in the case of Dirichlet boundary conditions, the existence of a solution with the constructed asymptotics is proved, and its Lyapunov asymptotic stability is studied. The proof of the theorems is based on the asymptotic method of differential inequalities developed by N.N. Nefedov.</p>

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Existence and Stability of a Stationary Solution with a Boundary Layer in a Two-Dimensional System of Fast and Slow Reaction–Diffusion–Advection Equations with KPZ Nonlinearities

  • 期刊论文

  • 发表日期：

    2025年6月1日

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  • A. O. Orlov

摘要

Abstract

The paper considers a boundary-value problem for a singularly perturbed elliptic system of fast and slow equations, commonly referred to as a system of Tikhonov type. A distinctive feature of the problem is the presence of terms containing the squared gradient of the unknown function (KPZ nonlinearities). A boundary layer asymptotic expansion of the solution is constructed in the case of Dirichlet boundary conditions, the existence of a solution with the constructed asymptotics is proved, and its Lyapunov asymptotic stability is studied. The proof of the theorems is based on the asymptotic method of differential inequalities developed by N.N. Nefedov.