Existence and nonexistence of solutions to the Hardy parabolic equation

2021/02/08 by Hisa, Kotaro, Sierżęga, Mikołaj · 1 citation
#35K15 #35K58 (Primary) 35A01 #35K67 #35R11(Secondary) #Analysis of PDEs (math.AP) #FOS: Mathematics

paper · doi:10.48550/arxiv.2102.04079

Abstract

In this paper, we obtain necessary conditions and sufficient conditions on the initial data for the local-in-time solvability of the Cauchy problem ∂_t u +(-Δ)^\fracθ2 u=|x|^-γ u^p , x∈\bf R^N, tgt;0, u(0)=μ in \bf R^N, where N≥ 1, 01, γ>0 and μ is a nonnegative Radon measure on \bf R^N. Using these conditions, we attempt to identify the optimal strength of the singularity of μ for the existence of solutions to this problem.

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