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

2020/12/10 by Yohei Fujishima, Kazuhiro Ishige, Fujishima, Yohei +1
Computer Science · Mathematics · #Advanced Mathematical Modeling in Engineering #Analysis of PDEs (math.AP) #FOS: Mathematics #Nonlinear Partial Differential Equations #Numerical methods in inverse problems

paper · pdf · doi:10.48550/arxiv.2012.05479

openalex publication_date 2020/12/10 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

Let (u,v) be a nonnegative solution to the semilinear parabolic system (P) \cases ∂_t u=D₁Δu+v^p, amp; x∈\bf R^N, tgt;0,
∂_t v=D₂Δv+u^q, amp; x∈\bf R^N, tgt;0,
(u(⋅,0),v(⋅,0))=(μ,ν), amp; x∈\bf R^N, where D₁, D₂>0, 01 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.

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