Non-uniqueness of solutions to the Cauchy problem for semilinear heat equations with singular initial data
Non-uniqueness of solutions to the Cauchy problem for semilinear heat equations with singular initial data
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DOI：
10.1007/s00208-004-0515-4
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发表时间：
2004-02
影响因子：
1.4
通讯作者：
Y. Naito
中科院分区：
文献类型：
--
作者：
Y. Naito
具有奇异初值的半线性热方程的Cauchy问题 其中N ≥2，λ>0为参数，且A ≥0，A ≥ 0.当p>（N+2）/N且（N-2）p<N+2时，存在一个正常数 使得问题有两个正的自相似解 和 与 如果 没有正的自相似解，如果 .此外，对于每个固定的 和 其中w 0是Haraux和Weissler构造的零初值问题的非唯一解.
The Cauchy problem for semilinear heat equations with singular initial data is studied, whereN≥2, λ>0 is a parameter, anda≥0,a≠0. We show that whenp>(N+2)/Nand (N−2)p<N+2, there exists a positive constant such that the problem has two positive self-similar solutions and with if and no positive self-similar solutions if . Furthermore, for each fixed and inL∞(RN) as λ→0, wherew0is a non-unique solution to the problem with zero initial data, which is constructed by Haraux and Weissler.