Global nonexistence of solutions for systems of quasilinear hyperbolic equations with damping and source terms

摘要

The initial boundary value problem for a class of quasilinear hyperbolic equations system in a bounded domain is studied. We prove that the solutions with positive initial energy blow up in finite time under some conditions. The estimates of the lifespan of solutions are given. MSC: 35A05, 35B40, 35L80.