{"title":"Riemann solutions and wave interactions for a hyperbolic system derived from the steady 2D Helmholtz equation under a paraxial assumption","authors":"Chun Shen","doi":"10.1016/j.aml.2024.109320","DOIUrl":null,"url":null,"abstract":"<div><div>Two kinds of exact Riemann solutions for a hyperbolic system arising from the steady 2D Helmholtz equation under a paraxial assumption are constructively achieved by using either delta shock wave or contact-vacuum-contact composite wave, which depends on the ordering relation between the left and right initial velocities. Moreover, the interaction between delta shock wave and contact-vacuum-contact composite wave is carefully explored by considering the initial data in three pieces separated by two jump discontinuities.</div></div>","PeriodicalId":55497,"journal":{"name":"Applied Mathematics Letters","volume":"160 ","pages":"Article 109320"},"PeriodicalIF":2.9000,"publicationDate":"2024-09-27","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"Applied Mathematics Letters","FirstCategoryId":"100","ListUrlMain":"https://www.sciencedirect.com/science/article/pii/S0893965924003409","RegionNum":2,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q1","JCRName":"MATHEMATICS, APPLIED","Score":null,"Total":0}
引用次数: 0
Abstract
Two kinds of exact Riemann solutions for a hyperbolic system arising from the steady 2D Helmholtz equation under a paraxial assumption are constructively achieved by using either delta shock wave or contact-vacuum-contact composite wave, which depends on the ordering relation between the left and right initial velocities. Moreover, the interaction between delta shock wave and contact-vacuum-contact composite wave is carefully explored by considering the initial data in three pieces separated by two jump discontinuities.
期刊介绍：
The purpose of Applied Mathematics Letters is to provide a means of rapid publication for important but brief applied mathematical papers. The brief descriptions of any work involving a novel application or utilization of mathematics, or a development in the methodology of applied mathematics is a potential contribution for this journal. This journal''s focus is on applied mathematics topics based on differential equations and linear algebra. Priority will be given to submissions that are likely to appeal to a wide audience.
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