Probabilistic approach to the heat equation with a dynamic Hardy-type potential

Izumi Okada and Eiji Yanagida

Stochastic Processes and their Applications, 2022, vol. 145, issue C, 204-225

Abstract: We consider the heat equation with a dynamic potential ∂∂tu=12Δu+V(x,t)u,x∈RN,where N>2. Here the potential V is given by a Hardy-type function V(x,t)=λ|x−ξ(t)|−μ with constants λ,μ>0, and the singular point ξ(t) is a path of the N-dimensional fractional Brownian motion with the Hurst exponent 0Keywords: Heat equation; Hardy-type potential; Dynamic singularity; Fractional Brownian motion (search for similar items in EconPapers)
Date: 2022
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DOI: 10.1016/j.spa.2021.12.006

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