Electronic Journal of Qualitative Theory of Differential Equations (Apr 2010)

On the viscous Burgers equation in unbounded domain

  • Juan Limaco,
  • Haroldo Rodrigues Clark,
  • L. A. Medeiros

DOI
https://doi.org/10.14232/ejqtde.2010.1.18
Journal volume & issue
Vol. 2010, no. 18
pp. 1 – 23

Abstract

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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 $\mathbb{R}\times(0,\infty)$. Some aspects associated with a Cauchy problem are presented in order to employ the approximations of Faedo-Galerkin in whole real line $\mathbb{R}$. This becomes possible due to the introduction of weight Sobolev spaces which allow us to use arguments of compactness in the Sobolev spaces.