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Quasi-subdifferential operators and evolution equations

Pages: 447 - 456, Issue special, November 2013

 Abstract        References        Full Text (316.1K)          

Masahiro Kubo - Department of Mathematics, Nagoya Institute of Technology, Gokiso-cho, Showa-ku, Nagoya 466-8555, Japan (email)

1 T. Aiki, Mathematical models including a hysteresis operator, in "Dissipative phase transitions" (eds. P. Colli et al.), Ser. Adv. Math. Appl. Sci. 71 (2006), 1-20.       
2 H. Attouch, Familles d'operateurs maximaux monotones et mesurabilite, Ann. Mat. Pura Appl. 120 (1979), 35-111.       
3 H. Attouch, P. Bénilan, A. Damlamian, C. Picard, Equations d'évolution avec condition unilatérale, C. R. Acad. Sci. Paris Ser. A, 279 (1974), 607-609.       
4 C. Baiocchi and A. Capelo, "Variational and quasivariational inequalities", Wiley-Interscience, Chichester, 1984.       
5 H. Brézis, Équations et inéquations non linéaires dans les espaces vectoriel en dualité, Ann. Inst. Fourier, 18 (1968), 115-175.       
6 H. Brézis, Problèmes unilatéraux, J. Math. Pure Appl. IX. Ser., 51 (1972), 1-168.       
7 H. Brézis, "Opérateurs Maximaux Monotones et Semi-Groupes de Contractions dans les Espaces de Hilbert", North-Holland, Amsterdam-London, 1973.       
8 F. E. Browder and P. Hess, Nonlinear mappings of monotone type in Banach spaces, J. Funct. Anal., 11 (1972), 251-294.       
9 P. Colli, N. Kenmochi and M. Kubo, A phase-field model with temperature dependent constraint, J. Math. Anal. Appl., 256 (2001), 668-685.       
10 J.-L. Joly and U. Mosco, À propos de l'existence et de la régularité des solutions de certaines inéquations quasi-variationnelles, J. Funct. Anal., 34 (1979), 107-137.       
11 R. Kano, N. Kenmochi and Y. Murase, Elliptic quasi-variational inequalities and applications, Discrete Contin. Dyn. Syst., 2009 Suppl. (2009), 583-591.       
12 R. Kano, N. Kenmochi and Y. Murase, Parabolic quasi-variational inequalities with nonlocal constraints, Adv. Math. Sci. Appl., 19 (2009), 565-583 .       
13 R. Kano, Y. Murase and N. Kenmochi, Nonlinear evolution equations generated by subdifferentials with nonlocal constraints Banach Center Publ., 86, Warsaw, 2009, 175-194.       
14 N. Kenmochi, Some nonlinear parabolic variational inequalities, Israel J. Math., 22 (1975), 304-331.       
15 N. Kenmochi, Solvability of nonlinear evolution equations with time-dependent constraints and applications, Bull. Fac. Educ., Chiba Univ. Part II, 30 (1981), 1-87.
16 N. Kenmochi, Monotonicity and compactness methods for nonlinear variational inequalities in "Handbook of Differential Equations" Stationary Partial Differential Equations, Vol. IV (ed. M. Chipot), Elsevier/North Holland, Amsterdam, (2007).       
17 N. Kenmochi, T. Koyama and G.H. Meyer, Parabolic PDEs with hysteresis and quasivariational inequalities, Nonlinear Anal., 34 (1998), 665-686.       
18 N. Kenmochi and M. Kubo, Periodic stability of flow in partially saturated porous media, in ''Free Boundary Value Problems", Int. Ser. Numer. Math., 95 (1990), 127-152.       
19 M. Kubo, Characterization of a class of evolution operators generated by time-dependent subdifferentials, Funkc. Ekvacioj, 32 (1989), 301-321.       
20 M. Kubo, A filtration model with hysteresis, J. Differ. Equations, 201 (2004), 75-98.       
21 M. Kubo and N. Yamazaki, Quasilinear parabolic variational inequalities with time-dependent constraints, Adv. Math. Sci. Appl., 15 (2005), 60-68.       
22 M. Kubo and N. Yamazaki, Elliptic-parabolic variational inequalities with time-dependent constraints, Discrete Contin. Dyn. Syst., 19 (2007), 335-354.       
23 M. Kubo, K. Shirakawa and N. Yamazaki, Variational inequalities for a system of elliptic-parabolic equations, J. Math. Anal. Appl., 387 (2012), 490-511.       
24 M. Ôtani, Nonmonotone perturbations for nonlinear parabolic equations associated with subdifferential operators J. Differential Equations, 46 (1982), 268-299.       
25 M. Ôtani, Nonlinear evolution equations with time-dependent constarints Adv. Math. Sci. Appl., 3 (1993/94), 383-399.       
26 A. Visintin, "Differential models of hysteresis", Springer-Verlag, Berlin, 1994.       
27 N. Yamazaki, Doubly nonlinear evolution equations associated with elliptic-parabolic free boundary problems, Discrete Contin. Dyn. Syst., 2005 Suppl. (2005), 920-920.       
28 Y. Yamada, On evolution equations generated by subdifferential operators, J. Fac. Sci., Univ. Tokyo, Sect. IA, 23 (1976), 491-515.       

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