Stochastic representation of solution to nonlocal-in-time diffusion
Analysis of PDEs
2018-10-23 v1
Abstract
The aim of this paper is to give a stochastic representation for the solution to a natural extension of the Caputo-type evolution equation. The nonlocal-in-time operator is defined by a hypersingular integral with a (possibly time-dependent) kernel function, and it results in a model which serves a bridge between normal diffusion and anomalous diffusion. We derive the stochastic representation for the weak solution of the nonlocal-in-time problem in case of nonsmooth data. We do so by starting from an auxiliary Caputo-type evolution equation with a specific forcing term. Numerical simulations are also provided to support our theoretical results.
Cite
@article{arxiv.1810.08788,
title = {Stochastic representation of solution to nonlocal-in-time diffusion},
author = {Qiang Du and Lorenzo Toniazzi and Zhi Zhou},
journal= {arXiv preprint arXiv:1810.08788},
year = {2018}
}
Comments
31 pages, 12 figures, submitted