Existence of weak positive solutions to a nonlinear PDE system around a triple phase boundary, coupling domain and boundary variables

Mo'tassem Al-arydah, Arian Novruzi

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4 Scopus citations

Abstract

We consider a 2D nonlinear system of PDEs representing a simplified model of processes near a triple-phase boundary (TPB) in cathode catalyst layer of hydrogen fuel cells. The particularity of this system is the coupling of a variable satisfying a PDE in the interior of the domain with another variable satisfying a differential equation (DE) defined only on the boundary, through an adsorption-desorption equilibrium mechanism. The system includes also an isolated singular boundary condition which models the flux continuity at the contact of the TPB with a subdomain. By freezing certain terms we transform the nonlinear PDE system to an equation, which has a variational formulation. We prove several L and W1,p a priori estimates and then by using Schauder fixed point theorem we prove the existence of a weak positive bounded solution.

Original languageBritish English
Pages (from-to)686-700
Number of pages15
JournalJournal of Mathematical Analysis and Applications
Volume382
Issue number2
DOIs
StatePublished - 15 Oct 2011

Keywords

  • PDEs
  • PEM fuel cells
  • Surface and bulk diffusions
  • Triple phase boundary
  • Variational problems

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