A model for assisted periodic breathing with degenerate permeability

The process of breathing is interpreted as forced periodic motion of a viscoelastic deformable porous medium with gas exchange between the interior and exterior, driven by forces acting on its boundary. Energy and mass are supplied to the system by muscle activity, and also possibly by external ventilation in case of assisted breathing for patients with lungs insufficiency. Hysteresis in the pressure–volume characteristic and possible degeneracy of the pressure-dependent terms are also taken into account. The main result consists in proving the existence of a periodic solution under arbitrary periodic forcing in suitable function spaces.