On viscosity solutions of space-fractional diffusion equations of Caputo type
Analysis of PDEs
2019-05-02 v1
Abstract
We study a fractional diffusion problem in the divergence form in one space dimension. We define a notion of the viscosity solution. We prove existence of viscosity solutions to the fractional diffusion problem with the Dirichlet boundary values by Perron's method. Their uniqueness follows from a proper maximum principle. We also show a stability result and basic regularity of solutions.
Keywords
Cite
@article{arxiv.1905.00168,
title = {On viscosity solutions of space-fractional diffusion equations of Caputo type},
author = {Tokinaga Namba and Piotr Rybka},
journal= {arXiv preprint arXiv:1905.00168},
year = {2019}
}