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The global Cauchy problem in Bourgain’s-type spaces for a dispersive dissipative semilinear equation. (English) Zbl 1011.35118
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:
35Q53KdV-like (Korteweg-de Vries) equations
35M10PDE of mixed type
35G25Initial value problems for nonlinear higher-order PDE