Global existence and blowup in infinite time for a fourth order wave equation with damping and logarithmic strain terms. (English) Zbl 1480.35045
Summary: We consider the well-posedness of solution of the initial boundary value problem to the fourth order wave equation with the strong and weak damping terms, and the logarithmic strain term, which was introduced to describe many complex physical processes. The local solution is obtained with the help of the Galerkin method and the contraction mapping principle. The global solution and the blowup solution in infinite time under sub-critical initial energy are also established, and then these results are extended in parallel to the critical initial energy. Finally, the infinite time blowup of solution is proved at the arbitrary positive initial energy.
MSC:
| 35B40 | Asymptotic behavior of solutions to PDEs |
| 35B44 | Blow-up in context of PDEs |
| 35B45 | A priori estimates in context of PDEs |
| 35L35 | Initial-boundary value problems for higher-order hyperbolic equations |
| 35L76 | Higher-order semilinear hyperbolic equations |
Keywords:
fourth order wave equation; Galerkin method; global existence; blowup in infinite time; arbitrary positive initial energyReferences:
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