GLOBAL NONEXISTENCE OF SOLUTION OF A SYSTEM WAVE EQUATIONS WITH NONLINEAR DAMPING AND SOURCE TERMS.

In this work, we consider the following system of nonlinear wave equations with nonlinear damping and source terms acting in both equations: u_tt - Δu_t - div (∇u∣^α-2∇u) - div (∣∇u_t∣^β1-2∇u_t) + a₁∣u_t∣^m-2u_t = ƒ₁(u,v), v_tt - Δv_t - div (∣∇v∣^α-2∇v) - div (∣v_t∣^β₂-2∇v_t) + a₂ ∣v_t∣^r-2 v_t = ƒ₂(u,v). Under an appropriate assumptions on the initial data and under some restrictions on the parameter α, β₁, β₂, m, r and on the nonlinear functions ƒ₁ and ƒ₂, we prove a global nonexistence result. Our method relies on the paper [20] where a different system of wave equations has been discussed. [ABSTRACT FROM AUTHOR]