SEMINAIRE D'ANALYSE NUMERIQUE
Année universitaire 2009-2010
Jeudi 8 octobre 2009 :
Arian NOVRUZI
(Université d'Ottawa)
Existence of bounded positive weak solutions to a nonlinear PDE system in a domain
with triple phase boundary (Exposé en français)
We consider a 2d nonlinear system of PDEs representing a simplified model of
reaction-diffusion processes near a triple-phase boundary in catalyst layer of
hydrogen fuel cells. This system couples variables defined in a two-phase domain
(the third phase is a solid one) and on the boundary, and including singular
boundary conditions. By fixing appropriately certain terms in the system we transform
it to a fixed point equation, which has a variationnal formulation.
We prove several L^\infty and W^{1,p} a priori estimates and using Schauder fixed point
theorem we prove the existence of a positive bounded weak solution.
This work is in collaboration with Motassem Alarydah.
