Asymptotic behavior of a weakly dissipative modified two-component Dullin-Gottwald-Holm system

In this paper, we consider the asymptotic behavior of a weakly dissipative modified two-component Dullin-Gottwald-Holm (mDGH2) system. We derive the asymptotic behavior of the solution at infinity expressed in exponential and algebraic forms. It is shown that there are some results about these properties of the strong solutions in L∞-space.