2002-Fez conference on Partial Differental Equations,
Electron. J. Diff. Eqns., Conf. 09, 2002, pp. 149-160.

### Local and global nonexistence of solutions to semilinear evolution equations Mohammed Guedda & Mokhtar Kirane

Abstract:
For a fixed and , such that , one main concern of this paper is to find sufficient conditions for non solvability of

posed in , where , with is the fractional power of the , and . The potential satisfies , for some positive . We shall see that the existence of solutions depends on the behavior at infinity of both initial data and the function or of both and . The non-global existence is also discussed. We prove, among other things, that if satisfies

any possible local solution blows up at a finite time for any locally integrable function . The situation is then extended to nonlinear hyperbolic equations.

Published December 28, 2002.
Subject classfications: 35K55, 35K65, 35L60.
Key words: Parabolic inequality, hyperbolic equation, fractional power, Fujita-type result.

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 Mohammed Guedda Universite de Picardie Jules Verne Faculte de Mathematiques et d'Informatique 33, rue Saint-Leu 80039 Amiens, France e-mail: Guedda@u-picardie.fr Mokthar Kirane Laboratoire de Mathematiques, Pole Sciences et Technologies, Universite de la Rochelle, Av. M. Crepeau, 17042 La Rochelle Cedex, France e-mail: mokhtar.kirane@univ-lr.fr