Anisotropic and isotropic persistent singularities of solutions of the fast diffusion equation
Anisotropic and isotropic persistent singularities of solutions of the fast diffusion equation
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DOI：
10.57262/die035-1112-729
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发表时间：
2021-11
影响因子：
1.4
通讯作者：
M. Fila;Petra Mackov'a;J. Takahashi;E. Yanagida
中科院分区：
文献类型：
--
作者：
M. Fila;Petra Mackov'a;J. Takahashi;E. Yanagida
抽象。研究了一类具有特殊持续奇异性的快扩散方程的正解。首先，我们构造了新的各向异性奇异解。根据参数的不同，这些解要么在分布意义上解原方程，要么它们在时空中不是局部可积的。我们证明了后者也适用于具有蛇形奇点的解，其存在性最近已被M。Fila，J.R. King、J. Takahashi和E.柳田此外，我们建立了在分布意义下，迷向解的存在性已由M。Fila、J.Takahashi和E. Yanagida在2019年，实际上解决了移动Dirac源项的相应问题。最后，我们讨论了临界情形下各向异性奇异解的存在性。
Abstract. The aim of this paper is to study a class of positive solutions of the fast diffusion equation with specific persistent singular behavior. First, we construct new types of solutions with anisotropic singularities. Depending on parameters, either these solutions solve the original equation in the distributional sense, or they are not locally integrable in space-time. We show that the latter also holds for solutions with snaking singularities, whose existence has been proved recently by M. Fila, J.R. King, J. Takahashi, and E. Yanagida. Moreover, we establish that in the distributional sense, isotropic solutions whose existence was proved by M. Fila, J. Takahashi, and E. Yanagida in 2019, actually solve the corresponding problem with a moving Dirac source term. Last, we discuss the existence of solutions with anisotropic singularities in a critical case.