On the viscous Burgers equation in unbounded domain

J. Limaco, Universidade Federal Fluminense, Niteroi-RJ, Brazil
H. Clark, Universidade Federal Fluminense, Niteroi-RJ, Brazil
L. A. Medeiros, UFRJ, Rio de Janeiro, Brasil

E. J. Qualitative Theory of Diff. Equ., No. 18. (2010), pp. 1-23.

Abstract: In this paper we investigate the existence and uniqueness of global solutions, and a rate stability for the energy related with a Cauchy problem to the viscous Burgers equation in unbounded domain $\re\times(0,\infty)$. Some aspects associated with a Cauchy problem are presented in order to employ the approximations of Faedo-Galerkin in whole real line $\re$. This becomes possible due to the introduction of weight Sobolev spaces which allow us to use arguments of compactness in the Sobolev spaces.

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