Filippo Dell’Oro , Lorenzo Liverani , Vittorino Pata , Ramon Quintanilla
{"title":"Global attractors for Moore–Gibson–Thompson thermoelastic extensible beams and Berger plates","authors":"Filippo Dell’Oro , Lorenzo Liverani , Vittorino Pata , Ramon Quintanilla","doi":"10.1016/j.nonrwa.2024.104298","DOIUrl":null,"url":null,"abstract":"<div><div>For <span><math><mrow><mi>p</mi><mo>∈</mo><mi>R</mi></mrow></math></span>, and <span><math><mrow><mi>α</mi><mo>,</mo><mi>β</mi><mo>,</mo><mi>γ</mi><mo>,</mo><mi>δ</mi><mo>,</mo><mi>η</mi><mo>></mo><mn>0</mn></mrow></math></span>, we consider an abstract version of the system <span><span><span><math><mfenced><mrow><mtable><mtr><mtd><msub><mrow><mi>u</mi></mrow><mrow><mi>t</mi><mi>t</mi></mrow></msub><mo>+</mo><msup><mrow><mi>Δ</mi></mrow><mrow><mn>2</mn></mrow></msup><mi>u</mi><mo>−</mo><mrow><mo>(</mo><mrow><mi>p</mi><mo>+</mo><msup><mrow><mo>‖</mo><mo>∇</mo><mi>u</mi><mo>‖</mo></mrow><mrow><mn>2</mn></mrow></msup></mrow><mo>)</mo></mrow><mi>Δ</mi><mi>u</mi><mo>=</mo><mi>η</mi><mi>Δ</mi><mrow><mo>(</mo><msub><mrow><mi>ϕ</mi></mrow><mrow><mi>t</mi><mi>t</mi></mrow></msub><mo>+</mo><mi>α</mi><msub><mrow><mi>ϕ</mi></mrow><mrow><mi>t</mi></mrow></msub><mo>)</mo></mrow><mo>+</mo><mi>f</mi><mspace></mspace></mtd></mtr><mtr><mtd><msub><mrow><mi>ϕ</mi></mrow><mrow><mi>t</mi><mi>t</mi><mi>t</mi></mrow></msub><mo>+</mo><mi>α</mi><msub><mrow><mi>ϕ</mi></mrow><mrow><mi>t</mi><mi>t</mi></mrow></msub><mo>−</mo><mi>β</mi><mi>Δ</mi><msub><mrow><mi>ϕ</mi></mrow><mrow><mi>t</mi></mrow></msub><mo>−</mo><mi>γ</mi><mi>Δ</mi><mi>ϕ</mi><mo>−</mo><mi>δ</mi><mi>Δ</mi><msub><mrow><mi>ϕ</mi></mrow><mrow><mi>t</mi><mi>t</mi></mrow></msub><mo>=</mo><mo>−</mo><mi>η</mi><mi>Δ</mi><msub><mrow><mi>u</mi></mrow><mrow><mi>t</mi></mrow></msub><mspace></mspace></mtd></mtr></mtable></mrow></mfenced></math></span></span></span>describing the dynamics of thermoelastic extensible beams or Berger plates, where the evolution of the temperature is ruled by a regularized Moore–Gibson–Thompson type equation. The existence of a global attractor of optimal regularity is proved.</div></div>","PeriodicalId":49745,"journal":{"name":"Nonlinear Analysis-Real World Applications","volume":"84 ","pages":"Article 104298"},"PeriodicalIF":1.8000,"publicationDate":"2024-12-27","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/S1468121824002372","RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q1","JCRName":"MATHEMATICS, APPLIED","Score":null,"Total":0}
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Abstract
For , and , we consider an abstract version of the system describing the dynamics of thermoelastic extensible beams or Berger plates, where the evolution of the temperature is ruled by a regularized Moore–Gibson–Thompson type equation. The existence of a global attractor of optimal regularity is proved.
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.
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