PreprintCC BY-NC-SA 4.0arXiv
Backward stochastic porous media equation with polynomial growth
Abstract
We investigate the well-posedness of a backward stochastic porous media equation whose nonlinear term is a polynomial operator corresponding to the slow diffusion regime. The main challenge stems from the structure of this nonlinear operator, which causes the operator to lose maximal monotonicity and prevents the use of standard weak-strong convergence techniques to identify the limit. Moreover, since the Laplace operator makes it difficult to separate the operators and discuss them individually, we attempt to obtain the of limit by investigating the global properties of the operator.
Related
- Solution to a fully coupled McKean-Vlasov forward-backward stochastic difference equation and applications to optimal control with law-delay
- Nonexistence of Stable Solutions to the Liouville Equation on Graphs with Polynomial Volume Growth
- Polynomial mixing for stochastic viscous conservation law equation on the whole line
- Polynomial mixing for the weakly damped stochastic nonlinear Schrödinger equation on the whole space
- Solutions of the space-fractional heat equation with polynomial growth: Liouville theorems and Schauder estimates
BibTeX
@misc{ciotir2026backward,
title = {{Backward stochastic porous media equation with polynomial growth}},
author = {Ioana Ciotir and Dan Goreac and Juan Li and Yufan Peng and Eduard Rotenstein},
howpublished = {arXiv},
year = {2026},
month = oct,
doi = {10.48550/arxiv.2610.21757},
eprint = {2610.21757},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2610.21757},
note = {CC BY-NC-SA 4.0},
}
RIS
TY - UNPB
TI - Backward stochastic porous media equation with polynomial growth
AU - Ioana Ciotir
AU - Dan Goreac
AU - Juan Li
AU - Yufan Peng
AU - Eduard Rotenstein
PY - 2026
DA - 2026/10/15
PB - arXiv
DO - 10.48550/arxiv.2610.21757
UR - https://arxiv.org/abs/2610.21757
AB - We investigate the well-posedness of a backward stochastic porous media equation whose nonlinear term is a polynomial operator corresponding to the slow diffusion regime. The main challenge stems from the structure of this nonlinear operator, which causes the operator to lose maximal monotonicity and prevents the use of standard weak-strong convergence techniques to identify the limit. Moreover, since the Laplace operator makes it difficult to separate the operators and discuss them individually, we attempt to obtain the of limit by investigating the global properties of the operator.
ER -