Global solutions and blow-up for the wave equation with variable coefficients. I: Interior supercritical source. (English) Zbl 1476.35045
Summary: In this paper, we consider the variable coefficient wave equation with damping and supercritical source terms. The goal of this work is devoted to prove the local and global existence, and classify decay rate of energy depending on the growth near zero on the damping term. Moreover, we prove the blow-up of the weak solution with positive initial energy as well as nonpositive initial energy.
MSC:
| 35B40 | Asymptotic behavior of solutions to PDEs |
| 35B44 | Blow-up in context of PDEs |
| 35L20 | Initial-boundary value problems for second-order hyperbolic equations |
| 35L71 | Second-order semilinear hyperbolic equations |
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