Global existence and blow up for damped generalized Boussinesq equation

Abstract

We study the Cauchy problem of damped generalized Boussinesq equation u tt − u xx + (u xx + f(u)) xx − αu xxt = 0. First we give the local existence of weak solution and smooth solution. Then by using potential well method and convexity method we prove the global existence and finite time blow up of solution, then we obtain some sharp conditions for the well-posedness problem.