PORTUGALIAE MATHEMATICA Vol. 59, No. 3, pp. 335349 (2002) 

KuramotoSivashinsky Equation in Domains with Moving BoundariesAlfredo Tadeu Cousin and Nickolai Andreevitch LarkineDepartment of Mathematics, State University of Maringá,Av. Colombo, 5790  CEP: 87020900, Maringá, PR  BRAZIL Email: atcousin@uem.br The Institute of Theoretical and Applied Mechanics, Novosibirsk  90, 630090  RUSSIA Email: nalarkin@dma.uem.br Abstract: In the noncylindrical domain ${Q}=\{(x,t); \alpha_1(t)<x<\alpha_2(t), t\in(0,T)\}$ we consider the initialboundary value problem for the onedimensional KuramotoSivashinsky equation $$ u_t+u\,u_x+\beta\,u_{xx}+\delta\,u_{xxxx}=0. $$ We prove the existence and uniqueness of global weak, strong and smooth solutions. The exponential decay of the solutions is also proved. Keywords: KuramotoSivashinsky equation; noncylindrical domains; Galerkin method. Classification (MSC2000): 35Q35, 35Q53. Full text of the article:
Electronic version published on: 9 Feb 2006. This page was last modified: 27 Nov 2007.
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