Global existence and blow-up of solutions for a system of Petrovsky equations. (English) Zbl 1375.35280
Summary: The initial-boundary value problem for a system of Petrovsky equations with memory and nonlinear source terms in bounded domain is studied. The existence of global solutions for this problem is proved by constructing a stable set, and obtain the exponential decay estimate of global solutions. Meanwhile, under suitable conditions on relaxation functions and the positive initial energy as well as non-positive initial energy, it is proved that the solutions blow up in the finite time and the lifespan estimates of solutions are also given.
MSC:
35L75 | Higher-order nonlinear hyperbolic equations |
35B40 | Asymptotic behavior of solutions to PDEs |
35L20 | Initial-boundary value problems for second-order hyperbolic equations |
35B44 | Blow-up in context of PDEs |