Tayeb Lakroumbe, M. Abdelli, Naima Louhibi, Mounir Bahlil
{"title":"具有非线性强耗散的Petrovsky方程解的适定性和一般能量衰减","authors":"Tayeb Lakroumbe, M. Abdelli, Naima Louhibi, Mounir Bahlil","doi":"10.24193/mathcluj.2021.2.13","DOIUrl":null,"url":null,"abstract":"We consider a nonlinear Petrovsky equation in a bounded domain with a strong dissipation, and prove the existence and the uniqueness of the solution using the energy method combined with the Faedo-Galerkin procedure under certain assumptions. Furthermore, we study the asymptotic behaviour of the solutions using a perturbed energy method.","PeriodicalId":39356,"journal":{"name":"Mathematica","volume":" ","pages":""},"PeriodicalIF":0.0000,"publicationDate":"2021-11-25","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":"{\"title\":\"Well-posedness and general energy decay of solutions for a Petrovsky equation with a nonlinear strong dissipation\",\"authors\":\"Tayeb Lakroumbe, M. Abdelli, Naima Louhibi, Mounir Bahlil\",\"doi\":\"10.24193/mathcluj.2021.2.13\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"We consider a nonlinear Petrovsky equation in a bounded domain with a strong dissipation, and prove the existence and the uniqueness of the solution using the energy method combined with the Faedo-Galerkin procedure under certain assumptions. Furthermore, we study the asymptotic behaviour of the solutions using a perturbed energy method.\",\"PeriodicalId\":39356,\"journal\":{\"name\":\"Mathematica\",\"volume\":\" \",\"pages\":\"\"},\"PeriodicalIF\":0.0000,\"publicationDate\":\"2021-11-25\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"0\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"Mathematica\",\"FirstCategoryId\":\"1085\",\"ListUrlMain\":\"https://doi.org/10.24193/mathcluj.2021.2.13\",\"RegionNum\":0,\"RegionCategory\":null,\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"Q4\",\"JCRName\":\"Mathematics\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"Mathematica","FirstCategoryId":"1085","ListUrlMain":"https://doi.org/10.24193/mathcluj.2021.2.13","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q4","JCRName":"Mathematics","Score":null,"Total":0}
Well-posedness and general energy decay of solutions for a Petrovsky equation with a nonlinear strong dissipation
We consider a nonlinear Petrovsky equation in a bounded domain with a strong dissipation, and prove the existence and the uniqueness of the solution using the energy method combined with the Faedo-Galerkin procedure under certain assumptions. Furthermore, we study the asymptotic behaviour of the solutions using a perturbed energy method.
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