$BV$-Estimates for Non-Linear Parabolic PDE with Linear Drift
Analysis of PDEs
2026-01-08 v1
Abstract
In the present work, we establish space Bounded Variation regularity of the solution for a non-linear parabolic partial differential equations involving a linear drift term. We study the problem in a bounded domain with mixed Dirichlet-Neumann boundary conditions, a general non-linearity and reasonable assumptions on the data. Our results also cover, as a particular case, the linear transport equation in a bounded domain with an outward-pointing drift vector field on the boundary.
Keywords
Cite
@article{arxiv.2601.03755,
title = {$BV$-Estimates for Non-Linear Parabolic PDE with Linear Drift},
author = {El Mahdi Erraji and Noureddine Igbida and Fahd Karami and Driss Meskine},
journal= {arXiv preprint arXiv:2601.03755},
year = {2026}
}