Asymptotic expansion for the generalized Benjamin-Bona-Mahony-Burger equation

Abstract

In this work we obtain the complete asymptotic expansion of solutions, as time goes to infinity, of both the linearized Benjamin-Bona-Mahony-Burger equation and the linear Korteweg-de Vries-Burger equation. We also compute the second term in the asymptotic expansion of the solution to the two-dimensional Benjamin-Bona-Mahony-Burger equation, with quadratic nonlinear term.