1
|
Franchi F, Nibbi R, Straughan B. Continuous dependence on modelling for temperature-dependent bidispersive flow. Proc Math Phys Eng Sci 2017. [DOI: 10.1098/rspa.2017.0485] [Citation(s) in RCA: 9] [Impact Index Per Article: 1.3] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/12/2022] Open
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.
Collapse
Affiliation(s)
- Franca Franchi
- Department of Mathematics, University of Bologna, 5 Piazza di Porta S. Donato, 40126 Bologna, Italy
| | - Roberta Nibbi
- Department of Mathematics, University of Bologna, 5 Piazza di Porta S. Donato, 40126 Bologna, Italy
| | - Brian Straughan
- Department of Mathematics, University of Durham, Durham DH1 3LE, UK
| |
Collapse
|