A non-stationary problem coupling PDEs and ODEs modelizing an automotive catalytic converter

Abstract

In this article we prove the existence and uniqueness of the solution of a non-stationary problem that modelizes the behavior of the concentrations and the temperature of gases going through a cylindrical passage of an automotive catalytic converter. This problem couples parabolic partial differential equations (PDEs) in a domain with one parabolic partial differential equation and some ordinary differential equations (ODEs) on a part of its boundary.

Keywords:

• Catalytic combustion
• Parabolic equation
• Ordinary differential equation
• Coupled system
• Transmission problem
• AMS: 35M10
• 35K65
• 35Q80

Acknowledgment

I would like to thank Professor Alain Brillard for giving me the subject of this paper for my PhD thesis, Professor Paul Deuring for his help in the proof of Lemma 4, Professor Samir Akesbi for his advice and Professor Bernard Brighi for many useful discussions.