Existence and Regularity of solutions to 1-D Fractional Order Diffusion Equations
Analysis of PDEs
2018-09-03 v1
Abstract
In this article we investigate the existence and regularity of 1-d steady state fractional order diffusion equations. Two models are investigated:the Riemann-Liouville fractional diffusion equation, and the Riemann-Liouville-Caputo fractional diffusion equation. For these models we explicitly show how the regularity of the solution depends upon the right hand side (rhs) function. We also establish for which Dirichlet and Neumann boundary conditions the models are well posed.
Keywords
Cite
@article{arxiv.1808.10555,
title = {Existence and Regularity of solutions to 1-D Fractional Order Diffusion Equations},
author = {Lueling Jia and Huanzhen Chen and V. J. Ervin},
journal= {arXiv preprint arXiv:1808.10555},
year = {2018}
}
Comments
22 pages