Nonexistence of backward self-similar blowup solutions to a supercritical semilinear heat equation
Nonexistence of backward self-similar blowup solutions to a supercritical semilinear heat equation
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超临界半线性热方程不存在后向自相似爆破解
DOI：
10.1016/j.jfa.2009.07.009
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发表时间：
2009
影响因子：
1.7
通讯作者：
N. Mizoguchi
中科院分区：
文献类型：
--
作者：
N. Mizoguchi
考虑一类半线性热方程的Cauchy问题，其中p> pS，其中pS是Sobolev指数.如果u（x，t）=（T-t）−1/（p−1）φ（（T-t）−1/2x），其中x∈ RN且t∈[0，T），其中φ是的正则正解，则u称为后向自相似爆破解。直接的是，对于所有p>1，（P）有平凡正解κ <$（p−1）−1/（p−1）。设PL为Lepin指数。当pS<p<pL时，Lepin得到了（P）的一个径向正则正解，除了κ.证明了当p>pL时，不存在空间非齐次的径向正则正解.
We consider a Cauchy problem for a semilinear heat equation with p>pSwhere pSis the Sobolev exponent. If u(x,t)=(T−t)−1/(p−1)φ((T−t)−1/2x) for x∈RNand t∈[0,T), where φ is a regular positive solution of then u is called a backward self-similar blowup solution. It is immediate that (P) has a trivial positive solution κ≡(p−1)−1/(p−1)for all p>1. Let pLbe the Lepin exponent. Lepin obtained a radial regular positive solution of (P) except κ for pS<p<pL. We show that there exist no radial regular positive solutions of (P) which are spatially inhomogeneous for p>pL.