Ahmed Noussair

Existence and uniqueness for a kinetic model of population dynamics with character dependence and spatial structure

this work, we consider a one species population dynamics model with character dependence, spatial structure and a nonlocal renewal process arising as a boundary condition. The individual interaction are based on Boltzmann kinetic-type modeling. Using fixed point arguments and the div-rot lemma, we prove that our model admits a unique global nonnegative solution.

Analysis of Nonlinear Resonance in Conservation Laws with Point Sources and Well‐Balanced Scheme

The purpose of this paper is to study the wave behavior of the hyperbolic conservation law with concatenation of point sources: formula math. for i ∈ I some finite index set, and where δ( ) is the Dirac measure. Special features of this problem are the discontinuities that appear along the t-axis at the point sources x = x i+1/2 . Resonance occurs when the speed of the nonlinear wave is close to zero. In addition to classical shock waves, the equation exhibits overcompressive and undercompressive waves. The Riemann problem with resonance is solved, and we show global existence via the Glimm scheme. Analytical understanding is used to design a well-balanced numerical scheme, of the Godunov type, which preserves the balance between the sources terms and the fluxes terms. Some numerical tests are reported.

Convergence of Numerical Schemes to a Nonlinear Kinetic Model of Population Dynamics with Nonlocal Boundary Conditions

We examine existence and uniqueness of a global solution and some basic mathematical issues associated with the development of a numerical scheme for a model of a tumor-immune system interaction. The system consists of nonlinear transport equations with a bilinear operator like a Boltzmann type and with a nonlocal boundary condition. We construct a numerical scheme as a combination of a

A reaction–diffusion system modeling predator–prey with prey-taxis

S(t)

Riemann Problem with Nonlinear Resonance Effects and Well-Balanced Godunov Scheme for Shallow Fluid Flow Past an Obstacle

-operator semigroup associated with the continuous problem and

Ecoviability for ecosystem-based fisheries management

P^\Delta

Global weak solution for a multi-stage physiologically structured population model with resource interaction

projection operator on the discrete space. The three estimates, (1)

Trajectory analysis of nonlinear kinetic models of population dynamics of several species

L^\infty

A reactiondiffusion system modeling predatorprey with prey-taxis

bound, (2) a uniform total variation bound, and (3)

On a population dynamic model of active cells with direct interaction

L^1