Finite time blow-up and global solutions for fourth order damped wave equations. (English) Zbl 1310.35046
Summary: This work is devoted to a class of fourth order wave equations with linear damping term and superlinear source term. After showing the uniqueness and existence of local solutions to the equations, we give necessary and sufficient conditions for global existence and finite time blow-up of these solutions. Moreover, the potential well depth is estimated.
MSC:
| 35B44 | Blow-up in context of PDEs |
| 35L76 | Higher-order semilinear hyperbolic equations |
| 35L35 | Initial-boundary value problems for higher-order hyperbolic equations |
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