Continuous dependence on modelling for temperature-dependent bidispersive flow

Franchi, Franca; Nibbi, Roberta; Straughan, Brian

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 20, 2018
• 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
• Public URL: https://durham-repository.worktribe.com/output/1337204