Seminar Details
2005-10-18 (14.00 pm) : Dynamical analysis of Plug Flow bioreactor nonlinear model
At Auditoire Euler
Organized by Mathematical Engineering
Speaker :
Abdou Dramé (CESAME)
Abstract :
This work deals with dynamical analysis of a
Plug Flow bioreactor in which occurs a growth reaction
(biomass/substrate). The dynamical modelling is based
on mass balance principles which leads to a system of
two autonomous partial differential equations. After a
linear change of variables, we prove that this system
is equivalent to an asymptotically autonomous
semilinear parabolic equation. We obtain convergence
result of solutions of the nonautonomous equation to
equilibrium solutions of its limit equation. In
addition the existence of multiple equilibrium
solutions is analyzed. The stress is laid on the non
monotonicity of the kinetic function and we prove that
the Plug Flow reactor can have one or multiple
equilibrium profiles according to the axial dispersion
and transport parameters. Numerical simulations
illustrate the bifurcation phenomena of the system.
The stability analysis of such equilibria proves that
in non degenerescence case, they are alternatively
stable, unstable, stable, etc.