An application of braid group theory to the finite time dead-core rate
An application of braid group theory to the finite time dead-core rate
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DOI：
10.1007/s00028-010-0072-0
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发表时间：
2010-05
影响因子：
1.4
通讯作者：
Jong-Shenq Guo;H. Matano;Chin-Chin Wu-Chin
中科院分区：
文献类型：
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作者：
Jong-Shenq Guo;H. Matano;Chin-Chin Wu-Chin
本文研究了球中具有强吸收的半线性热方程的正边值问题的死核问题。我们研究了死核率，即解到达第一个零点的速率。我们首先表明，在一维的情况下，死核心率总是快于自相似率。然后，利用一些特殊的解和辫群理论，我们得到了一个大类的初始数据的精确的死核率。
We consider the dead-core problem for the semilinear heat equation with strong absorption and with positive boundary values in a ball. We investigate the dead-core rate, i.e. the rate at which the solution reaches its first zero. We first show, as in the one-dimensional case, that the dead-core rate is always faster than the self-similar rate. By using some special solutions and the braid group theory, we then derive the exact dead-core rates for a large class of initial data.