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Gradient blowup solutions of a semilinear parabolic equation with exponential source

โœ Scribed by Zhang, Zhengce; Li, Yanyan

Book ID
125836627
Publisher
American Institute of Mathematical Sciences
Year
2012
Tongue
English
Weight
384 KB
Volume
12
Category
Article
ISSN
1534-0392

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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