On the global existence and blow-up for the double dispersion equation with exponential term

Abstract

This paper deals with the initial boundary value problem for the double dispersion equation with nonlinear damped term and exponential growth nonlinearity in two space dimensions. We first establish the local well-posedness in the natural energy space by the standard Galërkin method and contraction mapping principle. Then, we prove the solution is global in time by taking the initial data inside the potential well and the solution blows up in finite time as the initial data in the unstable set. Moreover, finite time blow-up results are provided for negative initial energy and for arbitrary positive initial energy respectively.

Keywords

• double dispersion equation
• nonlinear damped
• exponential nonlinearity
• global existence
• blow-up