{"title":"The Riemann problem for a generalised Burgers equation with spatially decaying sound speed. II General qualitative theory and numerical analysis","authors":"John Christopher Meyer, David John Needham","doi":"10.1016/j.nonrwa.2025.104349","DOIUrl":null,"url":null,"abstract":"<div><div>In this paper, we establish the global well-posedness of the Cauchy problem for a generalised viscous Burgers equation with spatially decaying sound speed, continuing from part I of this series of papers. Moreover, we establish qualitative properties, specifically bounds and monotonicity properties of solutions to the Cauchy problem. We also establish a conditional convergence result for an explicit mid-point finite difference scheme used throughout part I to approximate solutions to the Cauchy problem.</div></div>","PeriodicalId":49745,"journal":{"name":"Nonlinear Analysis-Real World Applications","volume":"85 ","pages":"Article 104349"},"PeriodicalIF":1.8000,"publicationDate":"2025-03-11","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"Nonlinear Analysis-Real World Applications","FirstCategoryId":"100","ListUrlMain":"https://www.sciencedirect.com/science/article/pii/S1468121825000355","RegionNum":3,"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
In this paper, we establish the global well-posedness of the Cauchy problem for a generalised viscous Burgers equation with spatially decaying sound speed, continuing from part I of this series of papers. Moreover, we establish qualitative properties, specifically bounds and monotonicity properties of solutions to the Cauchy problem. We also establish a conditional convergence result for an explicit mid-point finite difference scheme used throughout part I to approximate solutions to the Cauchy problem.
期刊介绍：
Nonlinear Analysis: Real World Applications welcomes all research articles of the highest quality with special emphasis on applying techniques of nonlinear analysis to model and to treat nonlinear phenomena with which nature confronts us. Coverage of applications includes any branch of science and technology such as solid and fluid mechanics, material science, mathematical biology and chemistry, control theory, and inverse problems.
The aim of Nonlinear Analysis: Real World Applications is to publish articles which are predominantly devoted to employing methods and techniques from analysis, including partial differential equations, functional analysis, dynamical systems and evolution equations, calculus of variations, and bifurcations theory.
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