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Sign-changing stationary solutions and blowup for the nonlinear heat equation in a ball

✍ Scribed by Thierry Cazenave; Flávio Dickstein; Fred B. Weissler

Book ID
105873541
Publisher
Springer
Year
2008
Tongue
English
Weight
269 KB
Volume
344
Category
Article
ISSN
0025-5831

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Critical Exponents for the Blowup of Sol
Critical Exponents for the Blowup of Solutions with Sign Changes in a Semilinear Parabolic Equation, II
✍ Noriko Mizoguchi; Eiji Yanagida 📂 Article 📅 1998 🏛 Elsevier Science 🌐 English ⚖ 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+2Â(k+1), k=0, 1, 2, ... , any solution with u 0 # 4 k blows up in finite time if 1 p k . T