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Zbl 1011.35118
Molinet, Luc; Ribaud, Francis
The global Cauchy problem in Bourgain's-type spaces for a dispersive dissipative semilinear equation. (English)
[J] SIAM J. Math. Anal. 33, No.6, 1269-1296 (2002). ISSN 0036-1410; ISSN 1095-7154/e

Summary: We prove local and global well-posedness results for the Kadomtsev-Petviashvili-Burgers equations in Bourgain's-type spaces. This approach is new for the study of semilinear evolution equations with a linear part which contains both dispersive and dissipative terms.
MSC 2000:
*35Q53 KdV-like equations
35M10 PDE of mixed type
35G25 Initial value problems for nonlinear higher-order PDE

Keywords: Kadomtsev-Petviashvili-Burgers equations; Bourgain spaces; global existence

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