On positive travelling wave solutions for a general class of KdV-Burger type equation

Journal of Nonlinear Sciences and Applications Pub Date : 2019-03-18 DOI:10.22436/JNSA.012.07.06

G. Arenas-Díaz, Jose R. Quintero

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.

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一类KdV-Burger型方程的正行波解

本文建立了三阶微分方程ut +αuxx +βuxxx + (f (x,u(x)))x = 0的正行波解的存在性，其中t, x∈R, f是一个具有某些性质的非负连续函数。该结果是将行波解描述为一些泛函的不动点的结果，使用与线性问题相关的格林函数定义，以及关于范数型锥展开和压缩的Krasnosel 'skii不动点定理。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

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来源期刊

Journal of Nonlinear Sciences and Applications MATHEMATICS, APPLIED-MATHEMATICS

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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.