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Life Span of Solutions for a Semilinear Parabolic Problem with Small Diffusion

โœ Scribed by Noriko Mizoguchi; Eiji Yanagida

Publisher
Elsevier Science
Year
2001
Tongue
English
Weight
134 KB
Volume
261
Category
Article
ISSN
0022-247X

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โœฆ Synopsis

where p > 1, ฮต > 0, is a bounded domain in R N , and ฯ• is a continuous function on . It is shown that the blowup time T ฮต of the solution of this problem satisfies T ฮต โ†’ 1 p-1 ฯ• 1-p โˆž as ฮต โ†’ 0. Moreover, when the maximum of ฯ• x is attained at one point, we determine the higher order term of T ฮต which reflects the pointedness of the peak of ฯ• . The proof is based on a careful construction of super-and subsolutions.

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