Advances in Differential Equations

The dynamics of chemical reactors in porous media

Johannes Bruining, Pablo Castañeda, and Dan Marchesin

Full-text: Access denied (no subscription detected) We're sorry, but we are unable to provide you with the full text of this article because we are not able to identify you as a subscriber. If you have a personal subscription to this journal, then please login. If you are already logged in, then you may need to update your profile to register your subscription. Read more about accessing full-text


Is ignition or extinction the fate of an exothermic chemical reaction occurring in a bounded region within a heat conductive solid consisting of a porous medium? In the spherical case, the reactor is modeled by a system of reaction-diffusion equations that reduces to a linear heat equation in a shell, coupled at the internal boundary to a nonlinear ODE modeling the reaction region. This ODE can be regarded as a boundary condition. This model allows the complete analysis of the time evolution of the system: there is always a global attractor. We show that, depending on physical parameters, the attractor contains one or three equilibria. The latter case has special physical interest: the two equilibria represent attractors ("extinction" or "ignition") and the third equilibrium is a saddle. The whole system is well approximated by a single ODE, a "reduced" model, justifying the "heat transfer coefficient" approach of Chemical Engineering.

Article information

Adv. Differential Equations Volume 17, Number 7/8 (2012), 725-746.

First available in Project Euclid: 17 December 2012

Permanent link to this document

Mathematical Reviews number (MathSciNet)

Zentralblatt MATH identifier

Primary: 35B38: Critical points 35B40: Asymptotic behavior of solutions 35K55: Nonlinear parabolic equations 35K575 35K60: Nonlinear initial value problems for linear parabolic equations 37L25: Inertial manifolds and other invariant attracting sets


Castañeda, Pablo; Marchesin, Dan; Bruining, Johannes. The dynamics of chemical reactors in porous media. Adv. Differential Equations 17 (2012), no. 7/8, 725--746.

Export citation