An Asymptotic Solution to a Nonlinear Reaction-Diffusion System with Chemotaxis

Abstract

We are concerned with a system of reaction-diffusion equations with chemotaxis with two types of components, the chemoattractant c and the attracted population b, in which the rate of degradation and the diffusion coefficient of the chemoattractant are low. This analysis is motivated by the applications in biology and ecology, related in particular to bioremediation of stratified media invaded by pollutants c. The system consists in n nonlinear parabolic equations with transmission conditions between layers for b. We shall prove the global in time existence of an asymptotic solution developed with respect to certain small parameters of the problem.

Keywords:

• Boundary value problems for nonlinear parabolic PDE
• Chemotaxis
• Perturbation method
• Reaction-diffusion system

Mathematics Subject Classification:

• 35K57
• 30E25
• 35B20
• 35K60

ACKNOWLEDGMENTS

G. Marinoschi acknowledges the support of CNCS-UEFISCDI project PCCE-55/2008, financed by the Romanian National Authority for Scientific Research.