Strong Convergence of Solutions and Attractors for Reaction-Diffusion Equations Governed by a Fractional Laplacian

IF 1.6 2区数学 Q2 MATHEMATICS, APPLIED

Applied Mathematics and Optimization Pub Date : 2025-03-08 DOI:10.1007/s00245-025-10242-w

Jiaohui Xu, Tomás Caraballo, José Valero

引用次数: 0

Abstract

A nonlocal reaction-diffusion equation governed by a fractional Laplace operator on a bounded domain is studied in this paper. First, the strong convergence of solutions of the equations governed by fractional Laplacian to the solutions of the classical equations governed by a standard Laplace operator is proved, when the fractional parameter grows to \(1\). Second, for the autonomous case, the upper semicontinuity of global attractors with respect to the attractors of the limit problem is established. Apparently, these are the first results for this kind of problems on bounded domains.

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分数阶拉普拉斯控制的反应扩散方程解和吸引子的强收敛性

研究了有界区域上分数阶拉普拉斯算子控制的非局部反应扩散方程。首先，证明了分数阶拉普拉斯算子控制的方程解对标准拉普拉斯算子控制的经典方程解的强收敛性，当分数阶参数增长到\(1\)时。其次，对于自治情况，建立了全局吸引子相对于极限问题的吸引子的上半连续性。显然，这是这类问题在有界域上的第一个结果。

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

Applied Mathematics and Optimization 数学-应用数学

CiteScore

3.30

自引率

5.60%

发文量

103

审稿时长

>12 weeks

期刊介绍： The Applied Mathematics and Optimization Journal covers a broad range of mathematical methods in particular those that bridge with optimization and have some connection with applications. Core topics include calculus of variations, partial differential equations, stochastic control, optimization of deterministic or stochastic systems in discrete or continuous time, homogenization, control theory, mean field games, dynamic games and optimal transport. Algorithmic, data analytic, machine learning and numerical methods which support the modeling and analysis of optimization problems are encouraged. Of great interest are papers which show some novel idea in either the theory or model which include some connection with potential applications in science and engineering.