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arXiv · 2012.05479

Optimal singularities of initial functions for solvability of a semilinear parabolic system

Yohei Fujishima·Kazuhiro Ishige
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Abstract

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.

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Yohei Fujishima, Kazuhiro Ishige. 2020-12-10. Optimal singularities of initial functions for solvability of a semilinear parabolic system. https://arxiv.org/abs/2012.05479

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