We prove global well-posedness for the Cauchy problem associated with the Kadomtsev-Petviashvili-Burgers equation (KPBII) in R2when the initial value belongs to the anisotropic Sobolev space Hs1, s2(R2) for all s1> - frac(1, 2) and s2≥ 0. On the other hand, we prove in some sense that our result is sharp. © 2007 Elsevier Inc. All rights reserved.
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