Abdou Khadry Dramé

Asymptotic Behavior and Stability for Solutions of a Biochemical Reactor Distributed Parameter Model

This paper deals with the dynamical analysis of a tubular biochemical reactor. The existence of nonnegative state trajectories and the invariance of the set of all physically feasible state values under the dynamical equation as well as the convergence of the state trajectories to equilibrium profiles are proved. In addition, the existence of multiple equilibrium profiles is analyzed. It is proved that, under physically meaningful conditions, the system has two stable and one unstable equilibrium profiles.

Multiple stable equilibrium profiles in tubular bioreactors

This paper deals with the existence and stability of multiple equilibrium profiles in tubular bioreactors. We prove here that a tubular biological reactor can posses one or several equilibrium profiles according to the dispersion and convection terms as long as the kinetic function belongs to a general class of non-monotonic functions. Such systems allow the characterization of the hydrodynamic behavior of most real systems in classifying them between completely mixed systems and perfect Plug Flow systems. The stability analysis of equilibrium profiles is also carried out and it is shown that they are alternatively stable, unstable, stable, etc.

On positive solutions of one-dimensional semipositone equations with nonlinear boundary conditions

a b s t r a c t In this note we show the existence of positive solutions for a one-dimensional class of semipositone boundary value problems with nonlinear boundary conditions. We study both the sublinear and superlinear situations by means of phase plane analysis.

Periodic trajectories of distributed parameter biochemical systems with time delay

Abstract This paper deals with a model of a biochemical reactor system with distributed parameters and with a time delay in the growth response. Time delay has been introduced in microbial growth systems to explain the time lapse between the consumption of (liquid) substrate and its conversion to (solid) biomass. We study here the properties of the resulting system of partial functional differential equations. We first prove the existence, positivity, and a compactness property of the system trajectories. We then prove the existence of periodic solutions of the system for large values of the delay. Numerical simulations illustrate the existence of such solutions.

Existence of nonnegative solution for a p-Laplacian semipositone problem with nonlinear boundary conditions

This paper studies the existence of nonnegative solution for a pLaplacian semipositone problem with nonlinear boundary conditions. Using variational techniques for locally Lipschitz functionals, we prove the existence of a nonnegative solution when the nonlinearity is superlinear and negative at the origin.

State Trajectories and Stability of Equilibria of a Distributed Parameter Biochemical Reactor

The dynamical analysis of a biochemical reactor distributed parameter nonlinear model is performed. The existence of nonnegative state trajectories and invariance of the set of all physically feasible state values under the dynamical equation, as well as the convergence of state trajectories to equilibrium profiles, are reported. In addition, it is reported that under physically meaningful conditions the system has two stable and one unstable equilibrium profiles