Global solutions and blow-up for a coupled system of nonlinear hyperbolic equations with weak damping. (English) Zbl 1527.35410
Summary: This paper investigates a coupled system of nonlinear hyperbolic equations with weak damping. It is shown that the global solution and finite time blow-up solution exist at subcritical or critical initial energy. Moreover, the finite time blow-up result at arbitrarily high initial energy is obtained. Also, we derive the exponential energy decay estimation of the global solution and estimate the upper and lower bounds of the blow-up time.
MSC:
| 35Q74 | PDEs in connection with mechanics of deformable solids |
| 35A01 | Existence problems for PDEs: global existence, local existence, non-existence |
| 35B44 | Blow-up in context of PDEs |
| 74H35 | Singularities, blow-up, stress concentrations for dynamical problems in solid mechanics |
| 74K05 | Strings |
| 74K10 | Rods (beams, columns, shafts, arches, rings, etc.) |
| 74H45 | Vibrations in dynamical problems in solid mechanics |
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