Nonexistence of global solutions of nonlinear wave equations.
Summary: In this paper the nonexistence of global solutions to wave equations of the type \[ u_{tt}-\Delta u\pm u_t=\lambda\,u + | u|^{1+q} \] is considered. We derive, for an averaging of solutions, a nonlinear second order differential inequality of the type \(w^{\prime\prime} \pm w^\prime \geq b\,w + | w|^{1+q}\), and we prove a blowing up phenomenon under some restriction on \(u(x,0)\) and \(u_t(x,0)\). Similar results are given for other equations.
scientific article; zbMATH DE number 1975348