Self-similar solutions of the second kind representing gelation in finite time for the Smoluchowski equation
Self-similar solutions of the second kind representing gelation in finite time for the Smoluchowski equation
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Smoluchowski 方程有限时间内凝胶化的第二类自相似解
DOI：
10.1088/0951-7715/27/7/1709
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发表时间：
2014
期刊：
影响因子：
1.7
通讯作者：
M. Fontelos
中科院分区：
文献类型：
--
作者：
G. Breschi;M. Fontelos
研究了具有核K（x，y）= x1−εy1−ε的Smoluchowski方程的自相似解，其中ε > 0，ε ≠ 1.证明了通过选择合适的相似指数作为ε的函数，自相似解在原点和无穷远处都具有正确的行为，这相当于求解了一个非线性特征值问题.这一特点的自相似的解决方案被发现是第二类的符号介绍巴伦布拉特。
We study the self-similar solutions of Smoluchowski's equation with kernel K(x, y) = x1−εy1−ε for ε > 0 and ε ≪ 1. We prove that by choosing the similarity exponents as suitable functions of ε, the self-similar solutions present correct behaviours at the origin and at infinity, which amounts to solving a nonlinear eigenvalue problem. This characterizes the self-similar solution found as being of the second kind in the notation introduced by Barenblatt.