Volume 54, Number 1, January-February 2020
|Page(s)||255 - 257|
|Published online||31 January 2020|
Periodic solutions of a hysteresis model for breathing
Università degli Studi di Modena e Reggio Emilia, Dipartimento di Scienze Fisiche, Informatiche e Matematiche, Via Campi 213/b, 41125 Modena, Italy
2 Mathematical Institute of the Silesian University, Na Rybnčku 1, 746 01 Opava, Czech Republic
3 Faculty of Civil Engineering, Czech Technical University, Thákurova 7, 16629 Praha 6, Czech Republic
4 Institute of Mathematics, Czech Academy of Sciences, Žitná 25, 11567 Praha 1, Czech Republic
* Corresponding author: firstname.lastname@example.org
Accepted: 21 August 2019
We propose to model the lungs as a viscoelastic deformable porous medium with a hysteretic pressure–volume relationship described by the Preisach operator. Breathing is represented as an isothermal time-periodic process with gas exchange between the interior and exterior of the body. The main result consists in proving the existence of a periodic solution under an arbitrary periodic forcing in suitable function spaces.
Mathematics Subject Classification: 35Q92 / 35B10 / 47J40
Key words: Hysteresis operators / periodic solutions / mammalian lungs / convergence scheme
© EDP Sciences, SMAI 2020
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