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Sign-changing stationary solutions and blowup for a nonlinear heat equation in dimension two

✍ Scribed by Dickstein, Flávio; Pacella, Filomena; Sciunzi, Berardino

Book ID
125338358
Publisher
Springer
Year
2014
Tongue
English
Weight
288 KB
Volume
14
Category
Article
ISSN
1424-3199

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✍ 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