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

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Abstract

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.

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Notes

  1. This particular condition can be seen as a one-dimensional version of either a full-slip or a no-slip boundary condition.

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Acknowledgements

All authors have been supported by Praemium Academiæ of Š. Nečasová. S. Chebbi (first version) was supported by by the Czech Science Foundation (GAČR) through project 19-04243 S. Further, V. Mácha and Š. Nečasová would like to announce the support from project GA22-01591S in the framework of the Czech Science Foundation. Finally, the Institute of Mathematics, CAS is supported in the framework of RVO:67985840.

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Authors and Affiliations

  1. Institute of Mathematics of the Czech Academy of Sciences, Žitná 25, 11567, Praha 1, Czech Republic

    Sabrine Chebbi, Václav Mácha & Šárka Nečasová

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  1. Sabrine Chebbi
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  2. Václav Mácha
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  3. Šárka Nečasová
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Correspondence to Šárka Nečasová.

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Chebbi, S., Mácha, V. & Nečasová, Š. Analysis of a system modeling the interaction between the motion of piston-spring and a viscous gas. Annali di Matematica 203, 903–925 (2024). https://doi.org/10.1007/s10231-023-01386-z

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