PreprintCC BY 4.0arXiv
Weak solutions to granular medium equations via stochastic particle approximations
Abstract
We establish weak existence for McKean--Vlasov stochastic differential equations associated with granular medium equations with porous medium diffusion, for m>1 in arbitrary dimension. The result covers a class of nonconvex potentials with locally Lipschitz gradients of polynomial growth. Our particle approximation generates nonlinear diffusion through density-dependent noise and allows initial densities with finite Boltzmann entropy but infinite internal energy.
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BibTeX
@misc{wodnicki2026weak,
title = {{Weak solutions to granular medium equations via stochastic particle approximations}},
author = {Łukasz Wodnicki},
howpublished = {arXiv},
year = {2026},
month = nov,
doi = {10.48550/arxiv.2611.05256},
eprint = {2611.05256},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2611.05256},
note = {CC BY 4.0},
}
RIS
TY - UNPB
TI - Weak solutions to granular medium equations via stochastic particle approximations
AU - Łukasz Wodnicki
PY - 2026
DA - 2026/11/03
PB - arXiv
DO - 10.48550/arxiv.2611.05256
UR - https://arxiv.org/abs/2611.05256
AB - We establish weak existence for McKean--Vlasov stochastic differential equations associated with granular medium equations with porous medium diffusion, for m>1 in arbitrary dimension. The result covers a class of nonconvex potentials with locally Lipschitz gradients of polynomial growth. Our particle approximation generates nonlinear diffusion through density-dependent noise and allows initial densities with finite Boltzmann entropy but infinite internal energy.
ER -