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Blow-Up of Solutions with Sign Changes for a Semilinear Diffusion Equation

โœ Scribed by Noriko Mizoguchi; Eiji Yanagida

Publisher
Elsevier Science
Year
1996
Tongue
English
Weight
117 KB
Volume
204
Category
Article
ISSN
0022-247X

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โœฆ Synopsis

0 with the Dirichlet, Neumann, or periodic boundary condition. Here ) 0 is a ลฝ . parameter, and f is an odd function of u satisfying f ะˆ 0 ) 0 and some convexity ลฝ . w x condition. Let z U be the number of times of sign changes for U g C 0, 1 . It is ร„ 4 shown that there exists an increasing sequence of positive numbers k ks0, 1, 2, . . . ลฝ . such that any solution with z u s k blows up in finite time if G , and there 0 k ลฝ . exists a global solution with z u s k if -.

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