Bin Yang , Yuming Qin , Alain Miranville , Ke Wang
{"title":"Existence and regularity of global attractors for a Kirchhoff wave equation with strong damping and memory","authors":"Bin Yang , Yuming Qin , Alain Miranville , Ke Wang","doi":"10.1016/j.nonrwa.2024.104096","DOIUrl":null,"url":null,"abstract":"<div><p>This paper is concerned with the existence and regularity of global attractor <span><math><mi>A</mi></math></span> for a Kirchhoff wave equation with strong damping and memory in <span><math><mi>H</mi></math></span> and <span><math><msup><mrow><mi>H</mi></mrow><mrow><mn>1</mn></mrow></msup></math></span>, respectively. In order to obtain the existence of <span><math><mi>A</mi></math></span>, 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 <span><math><mi>A</mi></math></span>.</p></div>","PeriodicalId":49745,"journal":{"name":"Nonlinear Analysis-Real World Applications","volume":null,"pages":null},"PeriodicalIF":1.8000,"publicationDate":"2024-03-15","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"Nonlinear Analysis-Real World Applications","FirstCategoryId":"100","ListUrlMain":"https://www.sciencedirect.com/science/article/pii/S1468121824000361","RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q1","JCRName":"MATHEMATICS, APPLIED","Score":null,"Total":0}
引用次数: 0
Abstract
This paper is concerned with the existence and regularity of global attractor for a Kirchhoff wave equation with strong damping and memory in and , respectively. In order to obtain the existence of , 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 .
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.