12 papers
A coupled prediction-correction Hughes' model for congested crowd motion
Hamza Ennaji, Noureddine Igbida, Ghadir Jradi +1
In this work, we introduce a new macroscopic model for crowd motion inspired by the celebrated Hughes' model \cite{Hughes2002, Hughes2003}, which couples a nonlinear conservation l…
-Estimates for Non-Linear Parabolic PDE with Linear Drift
El Mahdi Erraji, Noureddine Igbida, Fahd Karami +1
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.…
Mathematical Study of Reaction-Diffusion in Congested Crowd Motion
Noureddine Igbida, Fahd Karami, Driss Meskine
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 mot…
Congested Crossing Pedestrian Traffic Flow : Dispersion vs. Transport in Crowded Areas
Mariam Al Khatib, Said Gounane, Noureddine Igbida +1
This study investigates the complex dynamic interactions between two typed populations coexisting within a shared space. We propose both theoretical and numerical study to analyze…
Cross-Diffusion Theory for Overcrowding Dispersal in Interacting Species System
Noureddine Igbida
This work introduces a new class of cross-diffusion systems for studying overcrowding dispersal of two species. The approach, based on proximal minimization energy through a minimu…
Minimum Flow Steepest Descent Approach for Nonlinear PDE
Noureddine Igbida
This paper presents a minimum flow approach applicable to a wide range of doubly nonlinear diffusion problems. We introduce a minimum flow steepest descent algorithm that seeks an…
A granular model for crowd motion and pedestrian flow
Noureddine Igbida, José Miguel Urbano
We study a granular model for congested crowd motion and pedestrian flow. Our approach is based on an approximation through a Hele-Shaw type equation involving a degenerate operato…
Prediction-Correction Pedestrian Flow by Means of Minimum Flow Problem
Hamza Ennaji, Noureddine Igbida, Ghadir Jradi
We study a new variant of mathematical prediction-correction model for crowd motion. The prediction phase is handled by a transport equation where the vector field is computed via…
Theory for Incompressible Limit of Reaction-Diffusion Porous Medium Flow with Linear Drift
Noureddine Igbida
Our aim is to study the limit of the solution of reaction-diffusion porous medium equation with linear drift , as…
Quasi-convex Hamilton--Jacobi equations via limits of Finsler -Laplace problems as
Hamza Ennaji, Noureddine Igbida, Van Thanh Nguyen
In this paper we show that the maximal viscosity solution of a class of quasi-convex Hamilton--Jacobi equations, coupled with inequality constraints on the boundary, can be recover…
-Theory for Hele-Shaw flow with linear drift
Noureddine Igbida
The main goal of this paper is to prove -comparison and contraction principles for weak solutions (in the sense of distributions) of Hele-Shaw flow with a linear Drift. The fl…
On a Mathematical model for traveling sand dune
Noureddine Igbida, Fahd Karami, Driss Meskine
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 gr…