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On Critical Exponents for a Semilinear Parabolic System Coupled in an Equation and a Boundary Condition

✍ Scribed by Marek Fila; Howard A. Levine

Publisher: Elsevier Science
Year: 1996
Tongue: English
Weight: 242 KB
Volume: 204
Category: Article
ISSN: 0022-247X
DOI: 10.1006/jmaa.1996.0451

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✦ Synopsis

In this paper, we consider the system q 1 1 0 0 and bounded. We prove that if pq F 1 every nonnegative solution is global. When Ž . Ž . Ž . Ž . pq ) 1 we let ␣ s p q 2 r2 pq y 1 , ␤ s 2 q q 1 r2 pq y 1 . We show that if Ž . Ž . max ␣, ␤ ) Nr2 or max ␣, ␤ s Nr2 and p, q G 1, then all nontrivial nonnega-Ž . tive solutions are nonglobal; whereas if max ␣ , ␤ -Nr2 there exist both global and nonglobal nonnegative solutions.

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