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arXiv · 2601.03755

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

El Mahdi Erraji·Noureddine Igbida·Fahd Karami·Driss Meskine
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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.

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El Mahdi Erraji, Noureddine Igbida, Fahd Karami, Driss Meskine. 2026-01-07. $BV$-Estimates for Non-Linear Parabolic PDE with Linear Drift. https://arxiv.org/abs/2601.03755

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