具有强阻尼和记忆的基尔霍夫波方程全局吸引子的存在性和正则性

IF 1.8 3区数学 Q1 MATHEMATICS, APPLIED Nonlinear Analysis-Real World Applications Pub Date : 2024-03-15 DOI:10.1016/j.nonrwa.2024.104096

Bin Yang , Yuming Qin , Alain Miranville , Ke Wang

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引用次数: 0

摘要

本文主要研究在 H 和 H1 中分别具有强阻尼和强记忆的基尔霍夫波方程的全局吸引子 A 的存在性和正则性。为了得到 A 的存在性，我们主要采用能量法进行先验估计，然后用收缩函数法验证半群的渐近紧凑性。最后，通过将弱解分解为两部分和一些精细的计算，我们证明了 A 的正则性。

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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Existence and regularity of global attractors for a Kirchhoff wave equation with strong damping and memory

This paper is concerned with the existence and regularity of global attractor $A$ for a Kirchhoff wave equation with strong damping and memory in $H$ and $H^{1}$ , respectively. In order to obtain the existence of $A$ , we mainly use the energy method in the priori estimations, and then verify the asymptotic compactness of the semigroup by the method of contraction function. Finally, by decomposing the weak solutions into two parts and some elaborate calculations, we prove the regularity of $A$ .

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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.