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Finite time blow-up and global existence of weak solutions for pseudo-parabolic equation with exponential nonlinearity
Keywords:Pseudo-parabolic equation, Existence, Finite time blow-up, Exponential nonlinearity
      This paper is concerned with the initial value problem of a class of pseudo-parabolic equation u_t - \triangle u - \triangle u_t + u = f(u) with an exponential nonlinearity. The eigenfunction method and the Galerkin method are used to prove the blow-up, the local existence and the global existence of weak solutions. Moreover, we also obtain other properties of weak solutions by the eigenfunction method.