| Abstract: |
| In this talk, we investigate the existence of global attractor for a strongly damped wave equation with fully supercritical nonlinearities:
$ u_{tt}-\Delta u- \Delta u_t+h(u_t)+g(u)=f(x)$. In the case when the nonlinearities $h(u_t)$ and $g(u)$ are of fully supercritical growth, which leads to that the weak solutions of the equation lose their uniqueness, by introducing the notion of multi-valued operators, we establish some abstract criteria and use them to obtain the existence of global attractor of the equation in natural energy space in the sense of strong topology. Moreover, the geometrical structure of the global attractors of the corresponding multi-valued operators is shown. |
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