Nonexistence of Global Solutions of Nonlinear Wave Equations

R. Eloulaimi and M. Guedda

Abstract: In this paper the nonexistence of global solutions to wave equations of the type $u_{tt}-\Delta u\pm u_t=\lambda\,u + \vert u\vert^{1+q}$ is considered. We derive, for an averaging of solutions, a nonlinear second differential inequality of the type $w^{\prime\prime} \pm w^\prime \geq b\,w + \vert w\vert^{1+q}$, 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.

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