具有 KPZ 非线性的快速和慢速反应-扩散-对流方程系统中带有边界层的静态解的存在性和稳定性

IF 1 4区物理与天体物理 Q3 PHYSICS, MATHEMATICAL

Theoretical and Mathematical Physics Pub Date : 2024-07-27 DOI:10.1134/s0040577924070092

N. N. Nefedov, A. O. Orlov

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引用次数: 0

摘要

摘要在快速和慢速反应-扩散-对流方程中，研究了奇异扰动反应-扩散-对流方程组的静止解的存在性，这些方程组具有包含平方求函数梯度的非线性（KPZ 非线性）。微分不等式的渐近方法用于证明存在定理。在 Neumann 和 Dirichlet 边界条件情况下，构建了解的边界层渐近线。此外，还考虑了准单调源和无准单调性要求系统的情况。

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Existence and stability of stationary solutions with boundary layers in a system of fast and slow reaction–diffusion–advection equations with KPZ nonlinearities

Abstract

The existence of stationary solutions of singularly perturbed systems of reaction–diffusion–advection equations is studied in the case of fast and slow reaction–diffusion–advection equations with nonlinearities containing the gradient of the squared sought function (KPZ nonlinearities). The asymptotic method of differential inequalities is used to prove the existence theorems. The boundary layer asymptotics of solutions are constructed in the case of Neumann and Dirichlet boundary conditions. The case of quasimonotone sources and systems without the quasimonotonicity requirement is also considered.

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来源期刊

Theoretical and Mathematical Physics 物理-物理：数学物理

CiteScore

1.60

自引率

20.00%

发文量

103

审稿时长

4-8 weeks

期刊介绍： Theoretical and Mathematical Physics covers quantum field theory and theory of elementary particles, fundamental problems of nuclear physics, many-body problems and statistical physics, nonrelativistic quantum mechanics, and basic problems of gravitation theory. Articles report on current developments in theoretical physics as well as related mathematical problems. Theoretical and Mathematical Physics is published in collaboration with the Steklov Mathematical Institute of the Russian Academy of Sciences.