Finite time blow–up of solutions for system of $\kappa$th order wave equations with nonlinear averaged damping and sources

Abstract

We consider basic relationships between the initial energy and the exponent of nonlinear sources in a nonlinear coupled system of $\kappa$th order wave equations with nonlinear averaged damping, and we demonstrate the global nonexistence of solutions. This approach is a variant of the method of nonlinear functional analysis with a contradiction argument, which is one of the tools for proving the blow–up of solutions for nonlinear partial differential equations. A new class of nonlinear coupled wave equations with nonlinear sources is given in high-order functional spaces.