Solutions with time-dependent singular sets for the heat equation with absorption
Solutions with time-dependent singular sets for the heat equation with absorption
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带吸收的热方程的含时间相关奇异集的解
DOI：
10.1016/j.jde.2018.09.029
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发表时间：
2019
影响因子：
2.4
通讯作者：
Hikaru Yamamoto
中科院分区：
文献类型：
--
作者：
Jin Takahashi;Hikaru Yamamoto
考虑Rn中具有超线性吸收项的热方程<$t u− Δ u=− up，研究了具有m维时间依赖奇异集的非负解的存在性，其中n-m ≥ 3.证明了当1< p<（n-m）/（n-m-2）时，存在两类奇异解.此外，我们还证明了解的唯一性，并给出了解在奇异集附近的精确性态。
We consider the heat equation with a superlinear absorption term∂ t u− Δ u=− u p in R n and study the existence of nonnegative solutions with an m-dimensional time-dependent singular set, where n− m≥ 3. We prove that if 1< p<(n− m)/(n− m− 2), then there are two types of singular solutions. Moreover, we show the uniqueness of the solutions and specify the exact behavior of the solutions near the singular set.