Nonexistence of Global Solutions to Some Differential Inequalities of the Second Order and Applications

Philippe Souplet

Abstract: We establish the nonexistence of global nondecreasing positive solutions for a class of differential inequalities of the type $u''+u'^p \geq u^q$. As a consequence, we prove the non global character of the solutions for nonlinear wave equations of the type $u_{tt}-\Delta u+u_t=\lambda u+|u|^q$, when the initial data have positive projections on the first eigenvector and a similar result for a heat equation with memory.

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