Optimal Regularity in Time and Space for Nonlocal Porous Medium Type Equations
- Authors: Benjamin Gess, Jonas Sauer
- Preprint year: 2023
- First public date: 2023-11-10
- arXiv: 2311.06225
Abstract
A broad class of possibly non-unique generalized kinetic solutions to hyperbolic-parabolic PDEs is introduced. Optimal regularity estimates in time and space for such solutions to nonlocal, and spatially inhomogeneous variants of the porous medium equation are shown in the scale of Sobolev spaces. The optimality of these results is shown by comparison to the nonlocal Barenblatt solution. The regularity results are used in order to obtain existence of generalized kinetic solutions.
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BibTeX
@article{arxiv231106225,
title = {Optimal Regularity in Time and Space for Nonlocal Porous Medium Type Equations},
author = {Benjamin Gess and Jonas Sauer},
year = {2023},
eprint = {2311.06225},
archivePrefix = {arXiv},
primaryClass = {math.AP}
}