Mohammed Guedda & Mokhtar Kirane
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
| Mokthar Kirane |
Laboratoire de Mathematiques,
Pole Sciences et Technologies,
Universite de la Rochelle, Av. M. Crepeau,
17042 La Rochelle Cedex, France
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