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Blowup and Life Span of Solutions for a Semilinear Parabolic Equation

โœ Scribed by Mizoguchi, Noriko; Yanagida, Eiji

Book ID
118200226
Publisher
Society for Industrial and Applied Mathematics
Year
1998
Tongue
English
Weight
330 KB
Volume
29
Category
Article
ISSN
0036-1410

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๐Ÿ“œ SIMILAR VOLUMES

Life Span of Solutions for a Semilinear
Life Span of Solutions for a Semilinear Parabolic Problem with Small Diffusion
โœ Noriko Mizoguchi; Eiji Yanagida ๐Ÿ“‚ Article ๐Ÿ“… 2001 ๐Ÿ› Elsevier Science ๐ŸŒ English โš– 134 KB

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 whic

Critical Exponent for the Bipolar Blowup
Critical Exponent for the Bipolar Blowup in a Semilinear Parabolic Equation
โœ Noriko Mizoguchi; Hirokazu Ninomiya; Eiji Yanagida ๐Ÿ“‚ Article ๐Ÿ“… 1998 ๐Ÿ› Elsevier Science ๐ŸŒ English โš– 224 KB

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 suffici