V. Sobolev, E. Tropkina, E. Shchepakina, Lijun Zhang, Jundong Wang
{"title":"CRITICAL TRAVELLING WAVES IN ONE MODEL OF THE ”REACTION-DIFFUSION” TYPE","authors":"V. Sobolev, E. Tropkina, E. Shchepakina, Lijun Zhang, Jundong Wang","doi":"10.18287/2541-7525-2021-27-2-16-24","DOIUrl":null,"url":null,"abstract":"The paper is devoted to the order reduction for critical traveling wave problems for a reaction-diffusion type systems. The mathematical apparatus is based on the geometric theory of singular perturbations and the canards technique. The use of the method of invariant manifolds of singularly perturbed systems allows us to replace the study of traveling waves of the original PDE system by analyzing their profiles in a ODE system of a lower order.","PeriodicalId":427884,"journal":{"name":"Vestnik of Samara University. Natural Science Series","volume":"11 1","pages":"0"},"PeriodicalIF":0.0000,"publicationDate":"2022-03-30","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"Vestnik of Samara University. Natural Science Series","FirstCategoryId":"1085","ListUrlMain":"https://doi.org/10.18287/2541-7525-2021-27-2-16-24","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"","JCRName":"","Score":null,"Total":0}
引用次数: 0
Abstract
The paper is devoted to the order reduction for critical traveling wave problems for a reaction-diffusion type systems. The mathematical apparatus is based on the geometric theory of singular perturbations and the canards technique. The use of the method of invariant manifolds of singularly perturbed systems allows us to replace the study of traveling waves of the original PDE system by analyzing their profiles in a ODE system of a lower order.
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