Blow-up of solution for beam equation with delay and dynamic boundary conditions. (English) Zbl 1445.35090
Summary: In this paper, we consider an elastic beam equation with delay, source term, and boundary conditions together with some suitable initial data. Using the Faedo-Galerkin approximation and some estimates, we get the local existence of solution. Moreover, we obtain the finite time blow-up of solution by constructing suitable Lyapunov functionals.
MSC:
| 35B44 | Blow-up in context of PDEs |
| 35B35 | Stability in context of PDEs |
| 35L76 | Higher-order semilinear hyperbolic equations |
| 35L35 | Initial-boundary value problems for higher-order hyperbolic equations |
| 74K10 | Rods (beams, columns, shafts, arches, rings, etc.) |
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