Optimal singularities of initial functions for solvability of a semilinear parabolic system
Optimal singularities of initial functions for solvability of a semilinear parabolic system
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DOI：
10.2969/jmsj/86058605
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发表时间：
2020-12
影响因子：
0.7
通讯作者：
Y. Fujishima;Kazuhiro Ishige
中科院分区：
文献类型：
--
作者：
Y. Fujishima;Kazuhiro Ishige
设 $(u,v)$ 为半线性抛物线方程组的非负解 \[ \mbox{(P)} \qquad \cases{ \partial_t u=D_1\Delta u+v^p, & $x\in{\bf R}^N,\,\,\,t>0,$\\ \partial_t v=D_2\Delta v+u^q, & $x\in{\bf R}^N,\,\,\,t>0,$\\ (u(\cdot,0),v(\cdot,0))=(\mu,\nu), & $x\in{\bf R}^N,$ } \] 其中 $D_1$, $D_2>0$, $0 1$ 和 $(\mu,\nu)$ 是 ${\bf 中的一对非负氡测量或非负可测量函数R}^N$。在本文中，我们研究了问题~(P)可解的初始数据的充分条件，并阐明了可解的初始函数的最优奇点。
Let $(u,v)$ be a nonnegative solution to the semilinear parabolic system \[ \mbox{(P)} \qquad \cases{ \partial_t u=D_1\Delta u+v^p, & $x\in{\bf R}^N,\,\,\,t>0,$\\ \partial_t v=D_2\Delta v+u^q, & $x\in{\bf R}^N,\,\,\,t>0,$\\ (u(\cdot,0),v(\cdot,0))=(\mu,\nu), & $x\in{\bf R}^N,$ } \] where $D_1$, $D_2>0$, $0 1$ and $(\mu,\nu)$ is a pair of nonnegative Radon measures or nonnegative measurable functions in ${\bf R}^N$. In this paper we study sufficient conditions on the initial data for the solvability of problem~(P) and clarify optimal singularities of the initial functions for the solvability.