An equation related to the derivative Cahn–Hilliard equation with convection

IF 2.7 3区数学 Q1 MATHEMATICS, APPLIED

Physica D: Nonlinear Phenomena Pub Date : 2025-03-23 DOI:10.1016/j.physd.2025.134636

Renato Colucci

引用次数: 0

Abstract

We consider a nonlinear fourth order evolution equation related to the Convective Cahn–Hilliard equation. We study the asymptotic behaviour of the solutions and find the values of the parameters for which solutions converges to the zero steady state and no patterns are observed in the asymptotic behaviour. In other parameter’s regime we obtain the existence of a global attractor. Moreover we prove the existence of periodic travelling waves.

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一个与带对流的Cahn-Hilliard方程的导数有关的方程

我们考虑了一个与对流Cahn-Hilliard方程相关的非线性四阶演化方程。我们研究了解的渐近行为，并找到了解收敛于零稳态且在渐近行为中没有观测到模式的参数值。在其他参数区域，我们得到了全局吸引子的存在性。进一步证明了周期行波的存在性。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

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来源期刊

Physica D: Nonlinear Phenomena 物理-物理：数学物理

CiteScore

7.30

自引率

7.50%

发文量

213

审稿时长

65 days

期刊介绍： Physica D (Nonlinear Phenomena) publishes research and review articles reporting on experimental and theoretical works, techniques and ideas that advance the understanding of nonlinear phenomena. Topics encompass wave motion in physical, chemical and biological systems; physical or biological phenomena governed by nonlinear field equations, including hydrodynamics and turbulence; pattern formation and cooperative phenomena; instability, bifurcations, chaos, and space-time disorder; integrable/Hamiltonian systems; asymptotic analysis and, more generally, mathematical methods for nonlinear systems.