{"title":"Existence and Uniqueness of Solution for a Parabolic-Hyperbolic Equation with Multiplicative Control and Nonlocal Boundary Conditions","authors":"Volodymyr Kapustyan, Ivan Pyshnograiev","doi":"10.1007/s11253-024-02320-z","DOIUrl":null,"url":null,"abstract":"<p>We consider a parabolic-hyperbolic equation with multiplicative control and nonlocal boundary conditions. By using the Riesz biorthogonal basis, the problem is reduced to a sequence of one-dimensional problems with alternative representations of their solutions. Conditions guaranteeing the existence and uniqueness of the solution to the analyzed problem are established.</p>","PeriodicalId":0,"journal":{"name":"","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2024-08-17","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"","FirstCategoryId":"100","ListUrlMain":"https://doi.org/10.1007/s11253-024-02320-z","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"","JCRName":"","Score":null,"Total":0}
引用次数: 0
Abstract
We consider a parabolic-hyperbolic equation with multiplicative control and nonlocal boundary conditions. By using the Riesz biorthogonal basis, the problem is reduced to a sequence of one-dimensional problems with alternative representations of their solutions. Conditions guaranteeing the existence and uniqueness of the solution to the analyzed problem are established.
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