Analysis of a system modeling the interaction between the motion of piston-spring and a viscous gas

0584367 - MÚ 2025 RIV DE eng J - Journal Article
Chebbi, Sabrine - Mácha, Václav - Nečasová, Šárka
Analysis of a system modeling the interaction between the motion of piston-spring and a viscous gas.
Annali di Matematica Pura ed Applicata. Roč. 203, č. 2 (2024), s. 903-925. ISSN 0373-3114. E-ISSN 1618-1891
R&D Projects: GA ČR(CZ) GA22-01591S; GA ČR(CZ) GA19-04243S
Grant - others:AV ČR(CZ) AP2101
Program: Akademická prémie - Praemium Academiae
Institutional support: RVO:67985840
Keywords : boundary-value problems * global existence * fluid
OECD category: Pure mathematics
Impact factor: 1, year: 2022
Method of publishing: Limited access
https://doi.org/10.1007/s10231-023-01386-z

We are concerned with a one-dimensional flow of a compressible fluid which may be seen as a simplification of the flow of fluid in a long thin pipe. We assume that the pipe is on one side ended by a spring. The other side of the pipe is let open—there we assume either inflow or outflow boundary conditions. Such situation can be understood as a toy model for human lungs. We tackle the question of uniqueness and existence of a strong solution for a system modeling the above process, special emphasis is laid upon the estimate of the maximal time of existence.
Permanent Link: https://hdl.handle.net/11104/0352287