Global existence and asymptotic behavior of solutions to the generalized cubic double dispersion equation

Abstract

In this paper, we study the initial value problem for the generalized cubic double dispersion equation in n-dimensional space. Under a small condition on the initial data, we prove the global existence and asymptotic decay of solutions for all space dimensions n ≥ 1. Moreover, when n ≥ 2, we show that the solution can be approximated by the linear solution as time tends to infinity.