Fractional porous media equations: existence and uniqueness of weak solutions with measure data
Abstract
We prove existence and uniqueness of solutions to a class of porous media equations driven by the fractional Laplacian when the initial data are positive finite Radon measures on the Euclidean space. For given solutions without a prescribed initial condition, the problem of existence and uniqueness of the initial trace is also addressed. By the same methods we can also treat weighted fractional porous media equations, with a weight that can be singular at the origin, and must have a sufficiently slow decay at infinity (power-like). In particular, we show that the Barenblatt-type solutions exist and are unique. Such a result has a crucial role in [24], where the asymptotic behavior of solutions is investigated. Our uniqueness result solves a problem left open, even in the non-weighted case, in [42]
Keywords
Cite
@article{arxiv.1312.6076,
title = {Fractional porous media equations: existence and uniqueness of weak solutions with measure data},
author = {Gabriele Grillo and Matteo Muratori and Fabio Punzo},
journal= {arXiv preprint arXiv:1312.6076},
year = {2015}
}
Comments
Further results on initial traces added. Some proofs shortened