Multiple blowup of solutions for a semilinear heat equation
Multiple blowup of solutions for a semilinear heat equation
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DOI：
10.1007/s00208-004-0590-6
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发表时间：
2005-02
影响因子：
1.4
通讯作者：
N. Mizoguchi
中科院分区：
文献类型：
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作者：
N. Mizoguchi
本文研究一类半线性热方程的Cauchy问题 其中u0 ∈L∞（RN）.如果lim supt ≠ T，则称（P）的解att=T<+∞爆破|u（吨）|∞=+∞，上确界范数|·|∞在RN内。我们证明了如果 且N ≥11，则存在（P）的一个真解u，它爆破att=T1，成为∈（T1，T2）的一个正则解，并对某些T1，T2再次爆破att= T2，其中0<T1<T2<+∞。
The present paper is concerned with a Cauchy problem for a semilinear heat equation withu0∈L∞(RN). A solutionuof (P) is said to blow up att=T<+∞ if lim supt↗T|u(t)|∞=+∞ with the supremum norm |·|∞inRN. We show that if andN≥11, then there exists a proper solutionuof (P) which blows up att=T1, becomes a regular solution fort∈ (T1,T2) and blows up again att=T2for someT1,T2with 0<T1<T2<+∞.