| Abstract: |
| We consider the well-posedness and the longtime dynamics of the quasilinear wave equations with structural
damping and supercritical nonlinearities. We show that even for the supercritical nonlinearities, the solutions of the mentioned equations still possess parabolic-like characteristics because of the effectiveness of the structural damping. Furthermore, we obtain the existence of the global and exponential attractors (rather than the weak ones) in natural energy space. |
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