We study the following initial-boundary value problem for the Korteweg-de Vries-Burgers equation, 0 1where α = 0 1. We prove that if the initial data u 0 ∈ H 0 ω ∩ H 1 0 , where, and the norm u 0 H 0 ω + u 0 H 1 0 is sufficiently small, then there exists a unique solution u ∈ C 0 ∞ H . Moreover, if the initial data are such that, then there exists a constant A such that the solution has the asymptoticsfor t → ∞ uniformly with respect to x > 0 where α = 0 1, 0 q t = q/ √ π e −q 2 , 1 q t = 1/2 √ π √ t e −q 2 2q √ t − 1 + e −2q √ t . 2002 Elsevier Science
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