A free boundary problem describing reaction–diffusion problems in chemical vapor infiltration of pyrolytic carbon

Abstract

In this paper we consider chemical vapor deposition of pyrolytic carbon from methane in hot wall reactors. Especially, we deal with the interaction of homogeneous gas-phase and heterogeneous surface reactions. The resulting mathematical model is composed of a system of reaction–diffusion equations in a corner domain supplied with the Gibbs–Thomson law, which describes the movement of the free boundary, arising from the carbon deposition. We prove a short time existence and uniqueness result in Hölder spaces. We achieve this by contraction arguments and transforming the Gibbs–Thomson law to local coordinates to obtain a nonlinear parabolic equation on a manifold.