PreprintCC BY-NC-SA 4.0arXiv
Stochastic Porous Media Equations With Nonhomogeneous Dirichlet Boundary Conditions
Abstract
We aim at studying the well-posedness of stochastic porous media equation problems under nonhomogeneous Dirichlet boundary. We obtain an unconventional homogeneous Dirichlet boundary stochastic porous medium equation by transformation under an additional assumption, and then use approximation problems to obtain the well-posedness properties of the equation with homogeneous Dirichlet boundary conditions under different initial conditions. Consequently, we obtain the corresponding solution to the original equation.
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BibTeX
@misc{goreac2026stochastic,
title = {{Stochastic Porous Media Equations With Nonhomogeneous Dirichlet Boundary Conditions}},
author = {Dan Goreac and Ioana Ciotir and Juan Li and Yufan Peng},
howpublished = {arXiv},
year = {2026},
month = oct,
doi = {10.48550/arxiv.2610.11273},
eprint = {2610.11273},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2610.11273},
note = {CC BY-NC-SA 4.0},
}
RIS
TY - UNPB
TI - Stochastic Porous Media Equations With Nonhomogeneous Dirichlet Boundary Conditions
AU - Dan Goreac
AU - Ioana Ciotir
AU - Juan Li
AU - Yufan Peng
PY - 2026
DA - 2026/10/08
PB - arXiv
DO - 10.48550/arxiv.2610.11273
UR - https://arxiv.org/abs/2610.11273
AB - We aim at studying the well-posedness of stochastic porous media equation problems under nonhomogeneous Dirichlet boundary. We obtain an unconventional homogeneous Dirichlet boundary stochastic porous medium equation by transformation under an additional assumption, and then use approximation problems to obtain the well-posedness properties of the equation with homogeneous Dirichlet boundary conditions under different initial conditions. Consequently, we obtain the corresponding solution to the original equation.
ER -