Compactly supported solution of the time-fractional porous medium equation on the half-line
Analysis of PDEs
2018-03-12 v2
Abstract
In this work we prove that the time-fractional porous medium equation on the half-line with Dirichlet boundary condition has a unique compactly supported solution. The approach we make is based on a transformation of the fractional integro-differential equation into a nonlinear Volterra integral equation. Then, the shooting method is applied in order to facilitate the analysis of the free-boundary problem. We further show that there exists an exactly one choice of initial conditions for which the solution has a zero which guarantees the no-flux condition. Then, our previous considerations imply the unique solution of the original problem.
Keywords
Cite
@article{arxiv.1803.03016,
title = {Compactly supported solution of the time-fractional porous medium equation on the half-line},
author = {Łukasz Płociniczak and Mateusz Świtała},
journal= {arXiv preprint arXiv:1803.03016},
year = {2018}
}