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Continuous dependence on modelling for temperature-dependent bidispersive flow.

Franchi, Franca and Nibbi, Roberta and Straughan, Brian (2017) 'Continuous dependence on modelling for temperature-dependent bidispersive flow.', Proceedings of the Royal Society A : mathematical, physical and engineering sciences., 473 (2208). p. 20170485.


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.

Item Type:Article
Full text:(AM) Accepted Manuscript
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Date accepted:16 November 2017
Date deposited:20 March 2018
Date of first online publication:20 December 2017
Date first made open access:20 March 2018

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