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Proceedings of the American Mathematical Society
Proceedings of the American Mathematical Society
ISSN 1088-6826(online) ISSN 0002-9939(print)


On a semilinear parabolic equation

Author: Lotfi Riahi
Journal: Proc. Amer. Math. Soc. 135 (2007), 59-68
MSC (2000): Primary 35J60, 35K55
Published electronically: August 16, 2006
MathSciNet review: 2280175
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Abstract: We introduce a general class of potentials $ V=V(x,t)$ so that the semilinear parabolic equation $ a\Delta u-\frac \partial{\partial t} u+ V u^p =0$ in $ \mathbb{R}^n\times ]0,\infty[, n\geq 3,\, p>1$, $ a>0$, has global positive continuous solutions. These results extend the recent ones proved by Zhang to a more general class of potentials.

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Additional Information

Lotfi Riahi
Affiliation: Department of Mathematics, Faculty of Sciences of Tunis, Campus Universitaire, 2092 Tunis, Tunisia

PII: S 0002-9939(06)08730-2
Keywords: Parabolic equation, positive solution, fixed point theorem
Received by editor(s): June 30, 2004
Published electronically: August 16, 2006
Communicated by: David S. Tartakoff
Article copyright: © Copyright 2006 American Mathematical Society
The copyright for this article reverts to public domain 28 years after publication.