Blow-up of solutions to systems of nonlinear wave equations with supercritical sources

In this article, we focus on the life span of solutions to the following system of nonlinear wave equations: in a bounded domain Ω ⊂ ℝ n with Robin and Dirichlét boundary conditions on u and v, respectively. The nonlinearities f 1(u, v) and f 2(u, v) represent strong sources of supercritical order, while g 1(u t ) and g 2(v t ) represent interior damping. The nonlinear boundary condition on u, namely ∂ν u + u + g(u t ) = h(u) on Γ, also features h(u), a boundary source, and g(u t ), a boundary damping. Under some restrictions on the parameters, we prove that every weak solution to system above blows up in finite time, provided the initial energy is negative.