{"title":"Speed Selection of Traveling Waves of a Reaction–Diffusion–Advection Equation with High-Order Terms","authors":"Chaohong Pan, Shulin Hu, Hongyong Wang","doi":"10.1007/s12346-023-00923-8","DOIUrl":null,"url":null,"abstract":"<p>In this paper, we investigate the speed selection mechanism of traveling wave solutions for a reaction–diffusion–advection equation with high-order terms in a cylindrical domain. The study focuses the problem under two cases for Neumann boundary condition and Dirichlet boundary condition. By using the upper and lower solutions method, general conditions for both linear and nonlinear selections are obtained. When the equation is expanded to higher dimensions, literature examining this particular topic is scarce. In light of this, new results have been obtained for both linear and nonlinear speed selections of the equation with high-order terms. For different power exponents m and n, specific sufficient conditions for linear and nonlinear selections with the minimal wave speed are derived by selecting suitable upper and lower solutions. The impact of the power exponents m and n on speed selection is analyzed.</p>","PeriodicalId":48886,"journal":{"name":"Qualitative Theory of Dynamical Systems","volume":"11 1","pages":""},"PeriodicalIF":1.9000,"publicationDate":"2024-01-04","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"Qualitative Theory of Dynamical Systems","FirstCategoryId":"100","ListUrlMain":"https://doi.org/10.1007/s12346-023-00923-8","RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q1","JCRName":"MATHEMATICS","Score":null,"Total":0}
引用次数: 0
Abstract
In this paper, we investigate the speed selection mechanism of traveling wave solutions for a reaction–diffusion–advection equation with high-order terms in a cylindrical domain. The study focuses the problem under two cases for Neumann boundary condition and Dirichlet boundary condition. By using the upper and lower solutions method, general conditions for both linear and nonlinear selections are obtained. When the equation is expanded to higher dimensions, literature examining this particular topic is scarce. In light of this, new results have been obtained for both linear and nonlinear speed selections of the equation with high-order terms. For different power exponents m and n, specific sufficient conditions for linear and nonlinear selections with the minimal wave speed are derived by selecting suitable upper and lower solutions. The impact of the power exponents m and n on speed selection is analyzed.
本文研究了圆柱域中带有高阶项的反应-扩散-对流方程的行波解的速度选择机制。研究集中于 Neumann 边界条件和 Dirichlet 边界条件两种情况下的问题。通过使用上解和下解法，得到了线性和非线性选择的一般条件。当方程扩展到更高维度时，研究这一特定主题的文献很少。有鉴于此，我们获得了带有高阶项的方程线性和非线性速度选择的新结果。对于不同的功率指数 m 和 n，通过选择合适的上解和下解，得出了具有最小波速的线性和非线性选择的具体充分条件。分析了功率指数 m 和 n 对速度选择的影响。
期刊介绍：
Qualitative Theory of Dynamical Systems (QTDS) publishes high-quality peer-reviewed research articles on the theory and applications of discrete and continuous dynamical systems. The journal addresses mathematicians as well as engineers, physicists, and other scientists who use dynamical systems as valuable research tools. The journal is not interested in numerical results, except if these illustrate theoretical results previously proved.
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