半线性抛物方程的惯性流形在 Lipschitz 摄动下的稳定性

IF 1.8 3区数学 Q1 MATHEMATICS, APPLIED

Nonlinear Analysis-Real World Applications Pub Date : 2024-09-23 DOI:10.1016/j.nonrwa.2024.104219

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引用次数: 0

摘要

本文研究了半线性抛物方程惯性流形的稳定性和连续性。更确切地说，我们利用 Romanov (1994) 中讨论的 ODE 方法的非微观概括，证明了惯性流形的连续性以及反应扩散方程惯性流形上动力系统在域和方程的 Lipschitz 摄动下的 Gromov-Hausdorff 稳定性。

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Stability of inertial manifolds for semilinear parabolic equations under Lipschitz perturbations

In this paper we study the stability and continuity of inertial manifolds for semilinear parabolic equations. More precisely, we prove the continuity of inertial manifolds and the Gromov–Hausdorff stability of dynamical systems on inertial manifolds for reaction diffusion equations under Lipschitz perturbations of the domain and equation, using a nontrivial generalization of ODE approach discussed in Romanov (1994).

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来源期刊

Nonlinear Analysis-Real World Applications 数学-应用数学

CiteScore

3.80

自引率

5.00%

发文量

176

审稿时长

59 days

期刊介绍： Nonlinear Analysis: Real World Applications welcomes all research articles of the highest quality with special emphasis on applying techniques of nonlinear analysis to model and to treat nonlinear phenomena with which nature confronts us. Coverage of applications includes any branch of science and technology such as solid and fluid mechanics, material science, mathematical biology and chemistry, control theory, and inverse problems. The aim of Nonlinear Analysis: Real World Applications is to publish articles which are predominantly devoted to employing methods and techniques from analysis, including partial differential equations, functional analysis, dynamical systems and evolution equations, calculus of variations, and bifurcations theory.