Parabolic PDE with hysteresis

Control and Cybernetics

Volumn 25, Issue 3, 1996, Pages 631-643

  Showalter, Ralph E ^a   Little, Thomas D ^b   Hornung, Ulrich ^c  

^a UNIVERSITY OF TEXAS AT AUSTIN   (United States)

^b NEW YORK UNIVERSITY   (United States)

^c BUNDESWEHR UNIVERSITY MUNICH   (Germany)

Author keywords

Free boundary problem; Hysteresis; Memory; Phase change; Porous medium equation; Preisach model; Super Stefan problem

Indexed keywords

EID: 0030510343     PISSN: 03248569     EISSN: None     Source Type: Journal    
DOI: None     Document Type: Article

References (30)

1. ALT, H.W. (1985) On the thermostat problem. Control and Cybernetics 14, 171-193. Math. Z. 183 (1983), 311-341.
2. ALT, H.W. (1985) On the thermostat problem. Control and Cybernetics 14, 171-193. Math. Z. 183 (1983), 311-341.
3. BENILAN, PH. (1972) Équations d'évolution dans un espace de Banach quelconque et applications. Thesis, Orsay.
4. 1 existence and dependence results for semilinear elliptic equations under nonlinear boundary conditions. Appl. Math. Optim. 17, 203-224.
5. BREZIS, H. (1971) Monotonicity methods in Hilbert spaces and some application to nonlinear partial differential equations. In Contributions to Nonlinear Functional Analysis, (E.H. Zarantonello, ed.) Academic Press, New York.
6. BREZIS, H. (1973) Opérateurs Maximaux Monotones et Semigroupes de Contractions dans les Espaces de Hilbert, North Holland.
7. 1. J. Math. Soc. Japan 25, 15-26.
8. CARROLL, R.W. AND SHOWALTER, R.E. (1976) Singular and Degenerate Cauchy Problems. Academic Press, New York.
9. DUIJN, C. AND KNABNER, P. (1991) Solute transport in porous media with equilibrium and non-equilibrium multiple site adsorption: Travelling Waves. J. reine angew. Mathe. 415, 1-49.
10. HORNUNG, U. AND JÄGER, W. (1991) Homogenization of reactive transport through porous media. International Conference on Differential Equations Barcelona 1991 (Perelló C., Simó C., Solà-Morales, eds.), World Scientific Publishing, Singapore, 136-152.
11. HORNUNG, U. AND SHOWALTER, R.E. (1995) Elliptic-parabolic equations with hysteresis boundary conditions. SIAM Jour. Math. Analysis 26, 775-790.
12. HORNUNG, U. AND SHOWALTER, R.E. (1993) PDE-models with hysteresis on the boundary. In Models of Hysteresis (A. Visintin, ed.) Pitman Research Notes in Mathematics Series 286, 30-38.
13. KRASNOSEL'SKII, M.A. AND POKROVSKII, A.V. (1989) Systems with Hysteresis, Springer-Verlag, Berlin.
14. KREJCI, P. Hysteresis, Convexity and Dissipation in Hyperbolic Equations. Monograph in preparation.
15. LITTLE, T.D. AND SHOWALTER, R.E. (1995) The Super-Stefan problem. Int. J. Engng Sci 33, 67-75.
16. LITTLE, T.D. AND SHOWALTER, R.E. (1994) Semilinear parabolic equations with Preisach hysteresis. Diff. and Integral Equations 7, 1021-1040.
17. LITTLE, T.D. AND SHOWALTER, R.E. Vector hysteresis in PDE's, to appear.
18. LITTLE, T.D. (1993) Scmilinear Parabolic Equations with Prcisach Hysteresis. Dissertation, The University of Texas, June 1993.
19. MACKI, J.W., NISTRI, P. AND ZECCA, P. (1993) Mathematical models for hysteresis. SIAM Review 35, 94-123.
20. MAGENES, E. (1992) On a Stefan problem on the boundary of a domain. In Partial Differential Equations and Related Subjects (M. Miranda, ed.) Pitman Research Notes in Mathematics 269, Longman, 209-226.
21. MAYERGOYZ, I.D. (1991) Mathematical Models of Hysteresis, Springer, Berlin.
22. NEWCOMB, R.W. (1982) Semistate design theory: binary and swept hysteresis. Circuits, Systems and Signal Process 1, 203-216.
23. SHOWALTER, R.E. Maxwell's equations with hysteresis, in preparation.
24. SHOWALTER, R.E. AND WALKINGTON, N.J. (1990) A diffusion system for fluid in fractured media. Deferential and Integral Eqns. 3, 219-236.
25. VAN DER MERWE, A. J. (1998) B-evolutions and Sobolev equations. Applicable Analysis 29, 91-105.
26. VISINTIN, A. (1986) Evolution problems with hysteresis in the source term. SIAM J. Math. Anal. 17, 1113-1138.
27. VISINTIN, A. (1987) Partial differential equations with hysteresis. In Nonlinear Parabolic Equations: Qualitative Properties of Solutions (L. Boccardo, A. Tesci, eds.), Pitman, Boston, 226-232.
28. VISINTIN, A. (1993) Hysteresis and semigroups. In Models of Hysteresis (A. Visintin, ed.), Pitman Research Notes in Mathematics Series 286, 192-206.
29. VISINTIN, A. (1995) Differential Models of Hysteresis. Springer, Berlin.
30. VISINTIN, A. (1982) A phase transition problem with delay. Control and Cybernetics 11 (1982), 5-18.