{"title":"Global Solutions and Interactions of Non-selfsimilar Elementary Waves for n-D Non-homogeneous Burgers Equation","authors":"Yuan-an Zhao, Gao-wei Cao, Xiao-zhou Yang","doi":"10.1007/s10255-023-1097-9","DOIUrl":null,"url":null,"abstract":"<div><p>We investigate the global structures of the non-selfsimilar solutions for <i>n</i>-dimensional (<i>n</i>-D) non-homogeneous Burgers equation, in which the initial data has two different constant states, which are separated by a (<i>n</i> − 1)-dimensional sphere. We first obtain the expressions of <i>n</i>-D shock waves and rarefaction waves emitting from the initial discontinuity. Then, by estimating the new kind of interactions of the related elementary waves, we obtain the global structures of the non-selfsimilar solutions, in which ingenious techniques are proposed to construct the <i>n</i>-D shock waves. The asymptotic behaviors with geometric structures are also proved.</p></div>","PeriodicalId":6951,"journal":{"name":"Acta Mathematicae Applicatae Sinica, English Series","volume":"39 4","pages":"830 - 853"},"PeriodicalIF":0.9000,"publicationDate":"2023-11-08","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"Acta Mathematicae Applicatae Sinica, English Series","FirstCategoryId":"100","ListUrlMain":"https://link.springer.com/article/10.1007/s10255-023-1097-9","RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q3","JCRName":"MATHEMATICS, APPLIED","Score":null,"Total":0}
引用次数: 0
Abstract
We investigate the global structures of the non-selfsimilar solutions for n-dimensional (n-D) non-homogeneous Burgers equation, in which the initial data has two different constant states, which are separated by a (n − 1)-dimensional sphere. We first obtain the expressions of n-D shock waves and rarefaction waves emitting from the initial discontinuity. Then, by estimating the new kind of interactions of the related elementary waves, we obtain the global structures of the non-selfsimilar solutions, in which ingenious techniques are proposed to construct the n-D shock waves. The asymptotic behaviors with geometric structures are also proved.
期刊介绍:
Acta Mathematicae Applicatae Sinica (English Series) is a quarterly journal established by the Chinese Mathematical Society. The journal publishes high quality research papers from all branches of applied mathematics, and particularly welcomes those from partial differential equations, computational mathematics, applied probability, mathematical finance, statistics, dynamical systems, optimization and management science.