论文标题
初始功能的最佳奇异性，用于半连接抛物线系统的可溶性
Optimal singularities of initial functions for solvability of a semilinear parabolic system
论文作者
论文摘要
令$（u，v）$是半线性抛物线系统\ [\ mbox {（p）} \ qquad \案件{\ partial_t u =d_1Δu+v^p，＆$ x \ in {\ bf r} v =d_2Δv+u^q，＆$ x \ in {\ bf r}^n，\，\，\，\，\，\，t> 0，$ \\（u（\ cdot，0），v（\ cdot，0））=（μ，μ，ν），＆$ x \ in {\ bf r r} $ 0 <P \ le Q $带有$ pq> 1 $和$（μ，ν）$是一对非负rad ra尺寸或$ {\ bf r}^n $中的非负测量功能。在本文中，我们研究了最初数据的足够条件，以解决问题〜（p）的溶解度，并阐明了最初功能的最佳奇异性，以实现可溶性。
Let $(u,v)$ be a nonnegative solution to the semilinear parabolic system \[ \mbox{(P)} \qquad \cases{ \partial_t u=D_1Δu+v^p, & $x\in{\bf R}^N,\,\,\,t>0,$\\ \partial_t v=D_2Δv+u^q, & $x\in{\bf R}^N,\,\,\,t>0,$\\ (u(\cdot,0),v(\cdot,0))=(μ,ν), & $x\in{\bf R}^N,$ } \] where $D_1$, $D_2>0$, $0<p\le q$ with $pq>1$ and $(μ,ν)$ 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.
