On the viscous Burgers equation in unbounded domain | Zendy

J. Límaco | Zendy; H. R. Clark | Zendy; L. A. Medeiros | Zendy

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On the viscous Burgers equation in unbounded domain

Author(s) -

J. Límaco,

H. R. Clark,

L. A. Medeiros

Publication year - 2010

Publication title -

electronic journal of qualitative theory of differential equations

Language(s) - English

Resource type - Journals

SCImago Journal Rank - 0.524

H-Index - 33

ISSN - 1417-3875

DOI - 10.14232/ejqtde.2010.1.18

Subject(s) - mathematics , burgers' equation , domain (mathematical analysis) , mathematical analysis , calculus (dental) , partial differential equation , medicine , dentistry

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 R× (0,∞). Some aspects associated with a Cauchy problem are presented in order to employ the approximations of Faedo-Galerkin in whole real line R. 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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