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- W4226156611 abstract "In this paper we consider a non-local (in time) heat equation on a time-increasing parabolic set whose boundary is determined by a suitable curve. We provide a notion of solution for this equation and we study well-posedness under Dirichlet conditions outside the domain. A maximum principle is proved and used to derive uniqueness and continuity with respect to the initial datum of the solutions of the Dirichlet problem. Existence is proved by showing a stochastic representation based on the delayed Brownian motion killed on the boundary. Related properties on crossing probabilities of the delayed Brownian motion are obtained. The asymptotic behaviour of the mean square displacement of the process is determined, showing that the diffusive behaviour is anomalous." @default.
- W4226156611 created "2022-05-05" @default.
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- W4226156611 date "2022-03-18" @default.
- W4226156611 modified "2023-09-30" @default.
- W4226156611 title "Non-local heat equation with moving boundary and curve-crossing of delayed Brownian motion" @default.
- W4226156611 doi "https://doi.org/10.48550/arxiv.2203.09850" @default.
- W4226156611 hasPublicationYear "2022" @default.
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