Total versus single point blow-up of solutions of a semilinear parabolic equation with localized reaction
Total versus single point blow-up of solutions of a semilinear parabolic equation with localized reaction
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DOI：
10.1016/s0022-247x(03)00133-1
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发表时间：
2003-05
影响因子：
1.3
通讯作者：
Atsuko Okada;I. Fukuda
中科院分区：
文献类型：
--
作者：
Atsuko Okada;I. Fukuda
本文研究了具有局部化反应的半线性抛物型方程的初边值问题[公式：见正文]其中B是RN中的单位球，x ∈B，p，q>0.对于x ∈ N =0的情形，根据p和q的大小，我们将（P）的爆破解完全分为全爆破和单点爆破两类.此外，我们给出了解在爆破时刻附近的爆破速率。对于另一种情形x 0，我们证明了（P）解在某些情况下依赖于p和q的全爆破和单点爆破.
In this paper, we study the initial-boundary value problem of a semilinear parabolic equation with localized reaction, [Formula: see text] where B is a unit ball in RN, x∗∈B , and p,q>0. For the case x∗=0 , we completely classify blow-up solutions of (P) into total blow-up cases and single point blow-up cases according to the values p and q. Moreover, we give the blow-up rates of solutions near the blow-up time. For the other case x∗≠0 , we show total blow-up and single point blow-up of solutions of (P) in some cases depending on p and q.