Self-similar solution for Hardy operator

Self-similar solution for Hardy operator

We describe the large-time asymptotics of solutions to the heat equation for the fractional Laplacian with added subcritical or even critical Hardy-type potential. The asymptotics is governed by a self-similar solution of the equation, obtained as a normalized limit at the origin of the kernel of th...

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Veröffentlicht in:Journal of functional analysis 2023-09, Vol.285 (5), p.110014, Article 110014
Hauptverfasser: Bogdan, Krzysztof, Jakubowski, Tomasz, Kim, Panki, Pilarczyk, Dominika
Format: Artikel
Sprache:eng
Schlagworte:
Fractional Laplacian
Hardy potential
Self-similar solution
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Zusammenfassung:We describe the large-time asymptotics of solutions to the heat equation for the fractional Laplacian with added subcritical or even critical Hardy-type potential. The asymptotics is governed by a self-similar solution of the equation, obtained as a normalized limit at the origin of the kernel of the corresponding Feynman-Kac semigroup.
ISSN:0022-1236
1096-0783
DOI:10.1016/j.jfa.2023.110014