On exact dead-core rates for a semilinear heat equation with strong absorption
On exact dead-core rates for a semilinear heat equation with strong absorption
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DOI：
10.1142/s0219199711004154
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发表时间：
2011-02
影响因子：
1.6
通讯作者：
Yukihiro Seki
中科院分区：
文献类型：
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作者：
Yukihiro Seki
研究了RN中一类具有强吸收的半线性热方程ut = Δu - up，其中0 < p < 1.一个解决方案是已知的发展死核心在有限的时间为广泛的初始数据。我们构造具体的解决方案，准确的死核心速率比相应的常微分方程给出的。它们是通过匹配渐近展开技术和严格的拓扑不动点参数的先验估计的基础上，通过正式构造。为了得到先验估计，我们在一个新的函数空间中分析了一个线性化问题。
We study a semilinear heat equation with strong absorption ut = Δu - up with 0 < p < 1 in RN. A solution is known to develop dead-core in finite time for a wide class of initial data. We construct specific solutions with exact dead-core rates faster than the one given by the corresponding ODE. They are constructed formally by means of matched asymptotic expansion technique and rigorously by means of topological fixed-point arguments based on a priori estimates. To obtain the a priori estimates, we analyze a certain linearized problem in a new function space .