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Continuous dependence on modelling for temperature-dependent bidispersive flow

Franchi, Franca; Nibbi, Roberta; Straughan, Brian

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Authors

Franca Franchi

Roberta Nibbi

Brian Straughan



Abstract

We consider a model for flow in a porous medium which has a double porosity structure. There is the usual porosity herein called macro porosity, but in addition, we allow for a porosity due to cracks or fissures in the solid skeleton. The cracks give rise to a micro porosity. The model considered also allows for temperature effects with a single temperature T. This paper analyses three aspects of structural stability. The first establishes continuous dependence of the solution on the interaction coefficient between the velocities associated with the macro and micro porosity. The second analyses continuous dependence on the viscosity coefficients, while the third establishes continuous dependence on the radiation constant when Newton’s law of cooling is involved on the boundary.

Citation

Franchi, F., Nibbi, R., & Straughan, B. (2017). Continuous dependence on modelling for temperature-dependent bidispersive flow. Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences, 473(2208), Article 20170485. https://doi.org/10.1098/rspa.2017.0485

Journal Article Type Article
Acceptance Date Nov 16, 2017
Online Publication Date Dec 20, 2017
Publication Date Dec 20, 2017
Deposit Date Mar 20, 2018
Publicly Available Date Mar 29, 2024
Journal Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences
Print ISSN 1364-5021
Electronic ISSN 1471-2946
Publisher The Royal Society
Peer Reviewed Peer Reviewed
Volume 473
Issue 2208
Article Number 20170485
DOI https://doi.org/10.1098/rspa.2017.0485

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