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

Arenas-Díaz, Gilberto¹ ; Quintero, José R.²

¹ Escuela de Matematicas, Universidad Industrial de Santander, A.A. 678, Bucaramanga, Colombia
² Departamento de Matematicas, Universidad del Valle, A.A. 25360, Cali, Colombia

Journal of nonlinear sciences and its applications, Tome 12 (2019) no. 7, p. 485-502.

Résumé

In this paper, we establish the existence of positive traveling waves solutions for the third order differential equation $u_{t}+\alpha u_{xx}+\beta u_{xxx}+\left(f\left(x,u(x)\right)\right)_{x}=0$, where $t,x\in\bf R$, $f$ 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.

Détail

DOI : 10.22436/jnsa.012.07.06

Classification : 34G20, 35C07, 74J35
Keywords: Travelling wave solutions, Green function, Krasnosel'skii fixed point theorem

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