Work

$BV$-Estimates for Non-Linear Parabolic PDE with Linear Drift

Year: 2026

Type: preprint

Abstract: In the present work, we establish space Bounded Variation $(BV)$ 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.

Source: arXiv (Cornell University)

DOI: 10.48550/arxiv.2601.03755

Authors: Erraji, El Mahdi, Igbida, Noureddine, Karami, Fahd, Meskine, Driss

Institution: Cadi Ayyad University

Topic: Nonlinear Partial Differential Equations

Subfield: Applied Mathematics

Field: Mathematics

Domain: Physical Sciences

Open Access status: green

Funder: Centre National pour la Recherche Scientifique et Technique

OpenAlex ID: W7119512451

Cites:

Cited by:

Related to: