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Advances in Mathematical Physics
Volume 2015, Article ID 269536, 13 pages
http://dx.doi.org/10.1155/2015/269536
Research Article

Kawahara-Burgers Equation on a Strip

Departamento de Matemática, Universidade Estadual de Maringá, 87020-900 Maringá, PR, Brazil

Received 13 August 2015; Accepted 11 November 2015

Academic Editor: Mikhail Panfilov

Copyright © 2015 N. A. Larkin. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

Abstract

An initial-boundary value problem for the 2D Kawahara-Burgers equation posed on a channel-type strip was considered. The existence and uniqueness results for regular and weak solutions in weighted spaces as well as exponential decay of small solutions without restrictions on the width of a strip were proven both for regular solutions in an elevated norm and for weak solutions in the -norm.