{"title":"Well-Posedness and Blow-Up of Solutions for a Variable Exponent Nonlinear Petrovsky Equation","authors":"Nebi Yılmaz, Erhan Pişkin, Ercan Çelik","doi":"10.1155/2023/8866861","DOIUrl":null,"url":null,"abstract":"In this article, we investigate a nonlinear Petrovsky equation with variable exponent and damping terms. First, we establish the local existence using the Faedo–Galerkin approximation method under the conditions of positive initial energy and appropriate constraints on the variable exponents <svg height=\"12.7178pt\" style=\"vertical-align:-3.42947pt\" version=\"1.1\" viewbox=\"-0.0498162 -9.28833 19.8424 12.7178\" width=\"19.8424pt\" xmlns=\"http://www.w3.org/2000/svg\" xmlns:xlink=\"http://www.w3.org/1999/xlink\"><g transform=\"matrix(.013,0,0,-0.013,0,0)\"></path></g><g transform=\"matrix(.013,0,0,-0.013,7.71,0)\"></path></g><g transform=\"matrix(.013,0,0,-0.013,12.208,0)\"></path></g><g transform=\"matrix(.013,0,0,-0.013,15.172,0)\"></path></g></svg> and <span><svg height=\"12.7178pt\" style=\"vertical-align:-3.42947pt\" version=\"1.1\" viewbox=\"-0.0498162 -9.28833 18.5114 12.7178\" width=\"18.5114pt\" xmlns=\"http://www.w3.org/2000/svg\" xmlns:xlink=\"http://www.w3.org/1999/xlink\"><g transform=\"matrix(.013,0,0,-0.013,0,0)\"></path></g><g transform=\"matrix(.013,0,0,-0.013,6.383,0)\"><use xlink:href=\"#g113-41\"></use></g><g transform=\"matrix(.013,0,0,-0.013,10.881,0)\"><use xlink:href=\"#g113-46\"></use></g><g transform=\"matrix(.013,0,0,-0.013,13.845,0)\"><use xlink:href=\"#g113-42\"></use></g></svg>.</span> Finally, we prove a finite-time blow-up result for negative initial energy.","PeriodicalId":49111,"journal":{"name":"Advances in Mathematical Physics","volume":"17 6","pages":""},"PeriodicalIF":1.0000,"publicationDate":"2023-11-24","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"Advances in Mathematical Physics","FirstCategoryId":"101","ListUrlMain":"https://doi.org/10.1155/2023/8866861","RegionNum":4,"RegionCategory":"物理与天体物理","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q3","JCRName":"PHYSICS, MATHEMATICAL","Score":null,"Total":0}
引用次数: 0
Abstract
In this article, we investigate a nonlinear Petrovsky equation with variable exponent and damping terms. First, we establish the local existence using the Faedo–Galerkin approximation method under the conditions of positive initial energy and appropriate constraints on the variable exponents and . Finally, we prove a finite-time blow-up result for negative initial energy.
期刊介绍：
Advances in Mathematical Physics publishes papers that seek to understand mathematical basis of physical phenomena, and solve problems in physics via mathematical approaches. The journal welcomes submissions from mathematical physicists, theoretical physicists, and mathematicians alike.
As well as original research, Advances in Mathematical Physics also publishes focused review articles that examine the state of the art, identify emerging trends, and suggest future directions for developing fields.
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