{"title":"Method for the analysis of long water waves taking into account reflection from a gently sloping beach","authors":"D.A. Lozhnikov, V.E. Nazaikinskii","doi":"10.1016/j.jappmathmech.2017.07.003","DOIUrl":null,"url":null,"abstract":"<div><p>Algorithms and their software implementation are described that allow calculating the front propagation for a long wave (for example, a tsunami wave) described in the approximation of the linearized shallow water equations with reflection from a shallow beach taken into account. The algorithms are based on a construction of asymptotic solutions<span> of the Cauchy problem for hyperbolic equations with degeneracy on the boundary earlier proposed with the participation of one of the authors. The results of a numerical experiment are presented.</span></p></div>","PeriodicalId":49686,"journal":{"name":"Pmm Journal of Applied Mathematics and Mechanics","volume":"81 1","pages":"Pages 21-28"},"PeriodicalIF":0.0000,"publicationDate":"2017-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://sci-hub-pdf.com/10.1016/j.jappmathmech.2017.07.003","citationCount":"1","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"Pmm Journal of Applied Mathematics and Mechanics","FirstCategoryId":"1085","ListUrlMain":"https://www.sciencedirect.com/science/article/pii/S0021892817300394","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q3","JCRName":"Mathematics","Score":null,"Total":0}
引用次数: 1
Abstract
Algorithms and their software implementation are described that allow calculating the front propagation for a long wave (for example, a tsunami wave) described in the approximation of the linearized shallow water equations with reflection from a shallow beach taken into account. The algorithms are based on a construction of asymptotic solutions of the Cauchy problem for hyperbolic equations with degeneracy on the boundary earlier proposed with the participation of one of the authors. The results of a numerical experiment are presented.
期刊介绍：
This journal is a cover to cover translation of the Russian journal Prikladnaya Matematika i Mekhanika, published by the Russian Academy of Sciences and reflecting all the major achievements of the Russian School of Mechanics.The journal is concerned with high-level mathematical investigations of modern physical and mechanical problems and reports current progress in this field. Special emphasis is placed on aeronautics and space science and such subjects as continuum mechanics, theory of elasticity, and mathematics of space flight guidance and control.
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