We propose a model for breathing in the form of a PDE
system consisting of a mass balance equation and a momentum balance
equation. Lungs are represented by a viscoelastic porous body with
degenerate hysteretic pressure-saturation relation. We prove that
if a periodic force is applied on the boundary, then the resulting
system admits a periodic solution under suitable technical
assumptions. The proof relies on uniform bounds for the pressure
based on a time-periodic variant of the Moser-Alikakos iterations.
This is a joint work with M. Eleuteri, E. Ipocoana, and J. Kopfova.