Initial Boundary Value Problem Of Generalized Damped Boussinesq Equations With Exponential Growth

In this paper, we study the following initial boundary value problem of the generalized damped Boussinesq equation where f(s) is the given nonlinear function with exponential growth like es- at infinity, a,b,α,β> 0 are constants.By using Galerkin approximation scheme combined with the potential well and using Trudinger-Moser inequality, we prove the existence of global solution of the problem (1)-(3) if the initial data enter into a stable set. By constructing the unstable set, we give the sufficient condition of the nonexistence of the solution by modified convex method. Finally, we also give some examples of nonlinear functions with exponential growth at infinity.