Fractional heat equation involving Hardy-Leray Potential

2024/02/15 by Abdellaoui, Boumediene, Siclari, Giovanni, Primo, Ana
#35B25 #35B33 #35B44 #35K58 #47G20 #Analysis of PDEs (math.AP) #FOS: Mathematics

paper · doi:10.48550/arxiv.2402.09862

Abstract

In this paper we analyse the existence and non-existence of non-negative solutions to a non-local parabolic equation with a Hardy-Leray type potential. More precisely, we consider the problem \begincases (w_t-Δw)^s=\fracλ|x|^2s w+w^p +f, amp; in ℝ^N× (0,+∞),
w(x,t)=0, amp; in ℝ^N× (-∞,0], \endcases where N> 2s, 0p₊(λ,s). Then there are not any non-negative supersolutions. - Let p

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