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Critical Exponent for the Bipolar Blowup in a Semilinear Parabolic Equation

โœ Scribed by Noriko Mizoguchi; Hirokazu Ninomiya; Eiji Yanagida

Publisher
Elsevier Science
Year
1998
Tongue
English
Weight
224 KB
Volume
218
Category
Article
ISSN
0022-247X

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โœฆ Synopsis

It is shown that there exists a critical exponent p * > 1 for the bipolar blowup in the following sense. If 1 < p โ‰ค p * , then there exist arbitrarily small initial data such that the solution exhibits the bipolar blowup, whereas if p > p * , then the bipolar blowup does not occur for any sufficiently small initial data. The value of p * is expressed in terms of the dimension N and the second Dirichlet eigenvalue of the Laplace-Beltrami operator on โˆฉ S N-1 . In the case of

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