arXiv subjects

Fahd Karami

Publications and source records attributed to Fahd Karami.

4 recordsLinked to original sources

arXiv2026

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

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.

math.AP↗

arXiv2025

Mathematical Study of Reaction-Diffusion in Congested Crowd Motion

This paper establishes existence, uniqueness, and an L^1-comparison principle for weak solutions of a PDE system modeling phase transition reaction-diffusion in congested crowd motion. We consider a general reaction term and mixed homogeneous (Dirichlet and Neumann) boundary conditions. This model is applicable to various problems, including multi-species diffusion-segregation and pedestrian dynamics with congestion. Furthermore, our analysis of the reaction term yields sufficient conditions combining the drift with the reaction that guarantee the absence of congestion, reducing the dynamics to a constrained linear reaction-transport equation.

math.AP↗

arXiv2023

Mathematical analysis and multiscale derivation of a nonlinear predator-prey cross-diffusion--fluid system with two chemicals

A nonlinear cross-diffusion--fluid system with chemical terms describing the dynamics of predator-prey living in a Newtonian fluid is proposed in this paper. The existence of a weak solution for the proposed macro-scale system is proved based on the Schauder fixed-point theory, a priori estimates, and compactness arguments. The proposed system is derived from the underlying description delivered by a kinetic-fluid theory model by a multiscale approach. Finally, we discuss the computational results for the proposed macro-scale system in two-dimensional space.

math.AP↗

arXiv2021

On a Mathematical model for traveling sand dune

Our aim in this note is to introduce and study a mathematical model for the description of traveling sand dunes. We use surface flow process of sand under the effect of wind and gravity. We model this phenomena by a non linear diffusion-transport equation coupling the effect of transportation of sand due to the wind and the avalanches due to the gravity and the repose angle. The avalanche flow is governed by the evolution surface model and we use a nonlocal term to handle the transport of sand face to the wind.

math.AP↗