Asymptotic behavior for the Benjamin-Bona-Mahony equation in an exterior domain

Abstract

In this work we study the existence, uniqueness and asymptotic behavior in time of solutions for the dissipative Benjamin-Bona-Mahony equation in an exterior domain $\Omega \subset {{\mathbb R ^{n}}}$ ($n=2,3$). We obtain explicit polynomial decay rates for some norms of the solution which include the energy norm.