A semilinear parabolic boundary-value problem in bioreactors theory

Abstract

In this paper, we analyze a dynamical model describing the behavior of bioreactors with diffusion. We obtain a convergence result for solutions of asymptotically autonomous semilinear parabolic equations to steady state solutions of the limiting equations. This allows us to establish the convergence of solutions of the initial value problem that describes the dynamics of the bioreactor.