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Abstract <p> A singularly perturbed time-periodic boundary-value problem for a parabolic reaction–advection–diffusion equation with a nonlinearity containing the squared gradient of the unknown function (KPZ nonlinearity) is studied. A periodic solution with an internal transition layer is considered in the noncritical and critical cases. An asymptotic approximation of the solution is constructed, and the asymptotic behavior of a point of the transition layer is determined. Existence theorems and asymptotic stability are proved by the method of differential inequalities. </p>

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Periodic Contrast Structures in the Reaction–Diffusion–Advection Equation with a KPZ Nonlinearity

  • 期刊论文

  • 发表日期：

    2025年8月1日

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  • E. I. Nikulin,
  • A. O. Orlov

摘要

Abstract

A singularly perturbed time-periodic boundary-value problem for a parabolic reaction–advection–diffusion equation with a nonlinearity containing the squared gradient of the unknown function (KPZ nonlinearity) is studied. A periodic solution with an internal transition layer is considered in the noncritical and critical cases. An asymptotic approximation of the solution is constructed, and the asymptotic behavior of a point of the transition layer is determined. Existence theorems and asymptotic stability are proved by the method of differential inequalities.