Abstract
A new model for fluid flow in diatomites [3] motivates the study of a new degenerate parabolic system. We provide numerical as well as analytical evidence that there exists a free boundary, which represents the interface between the pristine rock and the damaged one.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
Preview
Unable to display preview. Download preview PDF.
References
G.I. Barenblatt, M. Bertsch, and C. Nitsch, Nonlocal damage accumulation and fluid flow in diatomites. Comm. App. Math. and Comp. Sci. 1 (2005), no. 1, 143–168.
G.I. Barenblatt, V.M. Entov, and Ryzhik V.M., Theory of fluid flows through natural rocks, Kluwer Academic Publishers, 1990.
G.I. Barenblatt, T.W. Patzek, V.M. Prostokishin, and D.B. Silin, Oil deposit in diatomites: a new challenge for subterranean mechanics, Society of Petroleum Engineers Thirteenth Symposium on Oil Recovery, 2002.
M. Bertsch R. Dal Passo, and C. Nitsch, A system of degenerate parabolic nonlinear PDE’s: a new free boundary problem, Interfaces Free Bound. 7 (2005), 255–276.
M. Bertsch and C. Nitsch, Traveling wave solutions of a nonlinear degenerate parabolic system from petroleum engineering, Preprint (2006).
R. Dal Passo, L. Giacomelli, and G. Grün, A waiting time phenomena for thin film equations, Ann. Scuola Norm. Sup. Pisa, XXX (2001), 437–463.
_____, Waiting time phenomena for degenerate parabolic equations — A unifying approach, Geometric Analysis and Nonlinear Partial Differential Equations (S. Hildebrant and H. Karcher, eds.), Springer-Verlag, 2003, pp. 637–648.
C. Nitsch, A nonlinear parabolic system arising in damage mechanics under chemical aggression, Nonlinear Anal. 61 (2005), no. 5, 695–713.
Author information
Authors and Affiliations
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2006 Birkhäuser Verlag Basel/Switzerland
About this paper
Cite this paper
Nitsch, C. (2006). A Free Boundary Problem for Nonlocal Damage Propagation in Diatomites. In: Figueiredo, I.N., Rodrigues, J.F., Santos, L. (eds) Free Boundary Problems. International Series of Numerical Mathematics, vol 154. Birkhäuser, Basel. https://doi.org/10.1007/978-3-7643-7719-9_33
Download citation
DOI: https://doi.org/10.1007/978-3-7643-7719-9_33
Published:
Publisher Name: Birkhäuser, Basel
Print ISBN: 978-3-7643-7718-2
Online ISBN: 978-3-7643-7719-9
eBook Packages: Mathematics and StatisticsMathematics and Statistics (R0)