Existence and convergence of solutions for the generalized BBM-burgers equations with dissipative term 2: the multidimensional case

Abstract

This paper is a continuation of our previous paper[16].It is concerned with the existence and convergence of the global smooth solutions for the multidimensional generalized BBM-Burgers equations with dissipative term

with initial data

Here, are constants,and are smooth vector-valuedfunctions. Some results on the global existence and convergence of the global smooth solutions for the Cauchy problem(1),(2)are obtained,and these results extend the results obtained in[16].

Keywords:

• BBM-Burgers equations
• entropy solutions
• strong convergence
• Sobolev imbedding theorem

AMS:

• 35L65
• 35Q53