{"title":"On positive travelling wave solutions for a general class of KdV-Burger type equation","authors":"G. Arenas-Díaz, Jose R. Quintero","doi":"10.22436/JNSA.012.07.06","DOIUrl":null,"url":null,"abstract":"In this paper, we establish the existence of positive traveling waves solutions for the third order differential equation ut +αuxx +βuxxx + (f (x,u(x)))x = 0, where t, x ∈ R, f is a non-negative continuous function with some properties. The result is a consequence of the characterization of the travelling wave solutions as fixed points of some functional, defined using the Green’s function associated to the linear problem, and the Krasnosel’skii fixed point theorem on cone expansion and compression of norm type.","PeriodicalId":48799,"journal":{"name":"Journal of Nonlinear Sciences and Applications","volume":"10 1","pages":""},"PeriodicalIF":0.0000,"publicationDate":"2019-03-18","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"Journal of Nonlinear Sciences and Applications","FirstCategoryId":"1085","ListUrlMain":"https://doi.org/10.22436/JNSA.012.07.06","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
In this paper, we establish the existence of positive traveling waves solutions for the third order differential equation ut +αuxx +βuxxx + (f (x,u(x)))x = 0, where t, x ∈ R, f is a non-negative continuous function with some properties. The result is a consequence of the characterization of the travelling wave solutions as fixed points of some functional, defined using the Green’s function associated to the linear problem, and the Krasnosel’skii fixed point theorem on cone expansion and compression of norm type.
期刊介绍：
The Journal of Nonlinear Science and Applications (JNSA) (print: ISSN 2008-1898 online: ISSN 2008-1901) is an international journal which provides very fast publication of original research papers in the fields of nonlinear analysis. Journal of Nonlinear Science and Applications is a journal that aims to unite and stimulate mathematical research community. It publishes original research papers and survey articles on all areas of nonlinear analysis and theoretical applied nonlinear analysis. All articles are fully refereed and are judged by their contribution to advancing the state of the science of mathematics. Manuscripts are invited from academicians, research students, and scientists for publication consideration. Papers are accepted for editorial consideration through online submission with the understanding that they have not been published, submitted or accepted for publication elsewhere.
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