{"title":"Global Well-posedness of Solutions for the $p$-Laplacian Hyperbolic Type Equation with Weak and Strong Damping Terms and Logarithmic Nonlinearity","authors":"N. Boumaza, Billel Gheraibia, Gongwei Liu","doi":"10.11650/tjm/220702","DOIUrl":null,"url":null,"abstract":". In this paper, we consider the p -Laplacian hyperbolic type equation with weak and strong damping terms and logarithmic nonlinearity. By using the potential well method and a logarithmic Sobolev inequality, we prove global existence, infinite time blow up and asymptotic behavior of solutions in two cases E (0) < d and E (0) = d . Furthermore, the infinite time blow up of solutions for the problem with E (0) > 0 ( ω = 0) is studied.","PeriodicalId":0,"journal":{"name":"","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2022-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"4","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"","FirstCategoryId":"100","ListUrlMain":"https://doi.org/10.11650/tjm/220702","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"","JCRName":"","Score":null,"Total":0}
引用次数: 4
Abstract
. In this paper, we consider the p -Laplacian hyperbolic type equation with weak and strong damping terms and logarithmic nonlinearity. By using the potential well method and a logarithmic Sobolev inequality, we prove global existence, infinite time blow up and asymptotic behavior of solutions in two cases E (0) < d and E (0) = d . Furthermore, the infinite time blow up of solutions for the problem with E (0) > 0 ( ω = 0) is studied.
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