| Volume 8, Number 1, 2018, Pages 105-122 DOI：10.11948/2018.105 |
| Finite time blow-up and global existence of weak solutions for pseudo-parabolic equation with exponential nonlinearity |
| Qunfei Long,Jianqing Chen,Ganshan Yang |
| Keywords:Pseudo-parabolic equation, existence, finite time blow-up, exponential nonlinearity. |
| Abstract: |
| This paper is concerned with the initial boundary 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. |
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