| Issue |
ESAIM: M2AN
Volume 54, Number 1, January-February 2020
|
|
|---|---|---|
| Page(s) | 255 - 257 | |
| DOI | https://doi.org/10.1051/m2an/2019060 | |
| Published online | 31 January 2020 | |
Periodic solutions of a hysteresis model for breathing
1
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: michela.eleuteri@unimore.it
Received:
1
February
2019
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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