A filtration model with hysteresis

Journal of Differential Equations

Volumn 201, Issue 1, 2004, Pages 75-98

  Kubo, Masahiro ^a  

^a SAGA UNIVERSITY   (Japan)

Author keywords

Filtration models; Hysteresis; Nonlinear PDEs; Parabolic PDEs; Quasi variational inequalities

Indexed keywords

EID: 2942655353     PISSN: 00220396     EISSN: None     Source Type: Journal    
DOI: 10.1016/j.jde.2004.02.010     Document Type: Article

References (24)

1. H.W. Alt, Strömungen durch inhomogene poröse Medien mit freiem Rand, J. Reine Angew. Math. 305 (1979) 89-115.
2. H.W. Alt, S. Luckhaus, A. Visintin, On nonstationary flow through porous media, Ann. Mat. Pura Appl. 136 (1984) 303-316.
3. H. Attouch, Mesurabilitè et monotonie, Publication Mathèmatique d'Orsay No. 183-76-53, Universitè Paris XI. U.E.R. Mathèmatique, Orsay, France, 1976.
4. F. Bagagiolo, Feedback control of a filtration problem with hysteresis, Adv. Math. Sci. Appl. 9 (1999) 787-804.
5. F. Bagagiolo, A. Visintin, Hysteresis in filtration through porous media, Z. Anal. Anwendungen 19 (2000) 977-997.
6. C. Baiocchi, A. Capelo, Variational and Quasivariational Inequalities, Wiley, New York, 1984.
7. J. Bear, Dynamics of Fluids in Porous Media, Dover, New York, 1972.
8. A. Beliaev, Positive solutions of the porous medium equation with hysteresis, J. Math. Anal. Appl. 281 (2003) 125-137.
9. A. Bensoussan, J.-L. Lions, Contrôle impulsionnel et inéquations quasi-variationnelles d'évolution, C. R. Acad. Sci. Paris Sér. A-B 276 (1973) 1333-1338.
10. H. Brézis, Opérateurs Maximaux Monotones et Semi-Groupes de Contractions dans les Espaces de Hilbert, North-Holland, Amsterdam-London-New York, 1973.
11. J. Carrillo, On the uniqueness of the solution of the evolution dam problem, Nonlinear Anal. TMA 22 (1994) 573-607.
12. P. Colli, K.H. Hoffmann, A nonlinear evolution problem describing multi-component phase changes with dissipation, Numer. Funct. Anal. Optim. 14 (1993) 275-297.
13. P. Colli, N. Kenmochi, M. Kubo, A phase field model with temperature dependent constraint, J. Math. Anal. Appl. 256 (2001) 668-685.
14. E. DiBenedetto, A. Friedman, Periodic behaviour for the evolutionary dam problem and related free boundary problems, Comm. Partial Differential Equations 11 (1986) 1297-1377.
15. G. Gilardi, A new approach to evolution free boundary problems, Comm. Partial Differential Equations 4 (1979) 1099-1123.
16. M. Hilpert, On uniqueness for evolution problems with hysteresis, in: J.-F. Rodrigues (Ed.), Mathematical Models for Phase Change Problems, Birkhäuser, Basel, 1989, pp. 377-388.
17. N. Kenmochi, M. Kubo, Periodic stability of flow in partially saturated porous media, in: K.-H. Hoffmann, J. Sprekels (Eds.), Free Boundary Problems (Oberwolfach, 1989), International Series of Numerical Mathematics, Vol. 95, Birkhäuser, Basel, 1990, pp. 127-152.
18. O.A. Ladyženskaja, V.A. Solonnikov, N.N. Ural'ceva, Linear and Quasilinear Equations of Parabolic Type, in: Translations of Mathematical Monographs, Vol. 23, American Mathematical Society, Providence RI, 1967.
19. J.L. Lions, Quelques Méthodes de Résolution des Problèmes aux Limites Non Linéaires, Dunod, Gouthiers-Villars, Paris, 1969.
20. J.L. Lions, E. Magenes, Non-Homogeneous Boundary Value Problems and Applications, Vol. I, Springer, New York, 1972.
21. F. Mignot, J.-P. Puel, Inéquations d'évolution paraboliques avec convexes dépendant du temps. Applications aux inéquations quasi variationnelles d'évolution, Arch. Rational Mech. Anal. 64 (1977) 59-91.
22. 1-contraction and uniqueness for unstationary saturated-unsaturated porous media flow, Adv. Math. Sci. Appl. 7 (1997) 537-553.
23. A. Visintin, Differential Models of Hysteresis, Springer, Berlin, 1994.
24. E. Zeidler, Nonlinear Functional Analysis and its Applications II/A Linear Monotone Operators, Springer, New York-Berlin, 1990.