{"title":"Global behavior of the solutions to nonlinear wave equations with combined power-type nonlinearities with variable coefficients","authors":"M. Dimova , N. Kolkovska , N. Kutev","doi":"10.1016/j.na.2024.113504","DOIUrl":null,"url":null,"abstract":"<div><p>In this paper we study the initial boundary value problem for the nonlinear wave equation with combined power-type nonlinearities with variable coefficients. Existence and uniqueness of local weak solutions are proved. The global behavior of the solutions with non-positive and sub-critical energy is completely investigated. The threshold between global existence and finite time blow up is found. For super-critical energy, two new sufficient conditions guaranteeing blow up of the solutions for a finite time, are given. One of them is proved for an arbitrary sign of the scalar product of the initial data, while the other one is derived only for a positive sign.</p></div>","PeriodicalId":49749,"journal":{"name":"Nonlinear Analysis-Theory Methods & Applications","volume":null,"pages":null},"PeriodicalIF":1.3000,"publicationDate":"2024-02-09","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"Nonlinear Analysis-Theory Methods & Applications","FirstCategoryId":"100","ListUrlMain":"https://www.sciencedirect.com/science/article/pii/S0362546X24000233","RegionNum":2,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q1","JCRName":"MATHEMATICS","Score":null,"Total":0}
引用次数: 0
Abstract
In this paper we study the initial boundary value problem for the nonlinear wave equation with combined power-type nonlinearities with variable coefficients. Existence and uniqueness of local weak solutions are proved. The global behavior of the solutions with non-positive and sub-critical energy is completely investigated. The threshold between global existence and finite time blow up is found. For super-critical energy, two new sufficient conditions guaranteeing blow up of the solutions for a finite time, are given. One of them is proved for an arbitrary sign of the scalar product of the initial data, while the other one is derived only for a positive sign.
期刊介绍:
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