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Initial-boundary value problems for a class of generalized KdV-Burgers equations. (Chinese. English summary) Zbl 0937.35164

Summary: This paper considers the initial-boundary value problem for the generalized KdV-Burgers equations with a third-order viscous term. Existence and uniqueness of a global solution are proved by means of a priori estimates and Galerkin method. The asymptotic behavior and “blow up” phenomenon of the solution are investigated under certain conditions.

MSC:

35Q53 KdV equations (Korteweg-de Vries equations)
35D05 Existence of generalized solutions of PDE (MSC2000)
35B40 Asymptotic behavior of solutions to PDEs
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