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Critical exponents for the blow-up of solutions with sign changes in a semilinear parabolic equation

โœ Scribed by Noriko Mizoguchi; Eiji Yanagida

Publisher
Springer
Year
1997
Tongue
English
Weight
168 KB
Volume
307
Category
Article
ISSN
0025-5831

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๐Ÿ“œ SIMILAR VOLUMES

Critical Exponents for the Blowup of Sol
Critical Exponents for the Blowup of Solutions with Sign Changes in a Semilinear Parabolic Equation, II
โœ Noriko Mizoguchi; Eiji Yanagida ๐Ÿ“‚ Article ๐Ÿ“… 1998 ๐Ÿ› Elsevier Science ๐ŸŒ English โš– 353 KB

The blowup of solutions of the Cauchy problem { u t =u xx + |u| p&1 u u(x, 0)=u 0 (x) in R\\_(0, ), in R is studied. Let 4 k be the set of functions on R which change sign k times. It is shown that for p k =1+2ร‚(k+1), k=0, 1, 2, ... , any solution with u 0 # 4 k blows up in finite time if 1 p k . T

Blow-Up of Solutions with Sign Changes f
Blow-Up of Solutions with Sign Changes for a Semilinear Diffusion Equation
โœ Noriko Mizoguchi; Eiji Yanagida ๐Ÿ“‚ Article ๐Ÿ“… 1996 ๐Ÿ› Elsevier Science ๐ŸŒ English โš– 117 KB

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 sequenc