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Strong solutions for parabolic variational inequalities. (English) Zbl 0395.35045

MSC:
35K55 Nonlinear parabolic equations
35G10 Initial value problems for linear higher-order PDEs
35K25 Higher-order parabolic equations
35A15 Variational methods applied to PDEs
35R20 Operator partial differential equations (= PDEs on finite-dimensional spaces for abstract space valued functions)
49S05 Variational principles of physics
Citations:
Zbl 0252.47055
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References:
[1] Brezis, H., Opérateurs marimaux monotones dans LES espaces de Hilbert et équations d’évolution, ()
[2] Kato, T., Nonlinear semi-groups and evolution equations, J. math. soc. Japan, 19, 508-520, (1967) · Zbl 0163.38303
[3] Crandall, M.; Pazy, A., Nonlinear evolution equations in Banach spaces, Israel J. math., 11, 57-94, (1972) · Zbl 0249.34049
[4] Martin, R.H., Generating an evolution system in a class of uniformly convex Banach spaces, J. funct. anal., 11, 62-76, (1972) · Zbl 0249.47065
[5] Watanabe, J., On certain nonlinear evolution equations, J. math. soc. Japan, 25, 446-463, (1973) · Zbl 0253.35053
[6] Attouch, H.; Damlamian, A., Problèmes d’évolution dans LES Hilbert et applications, J. math. pures appl., 54, 53-74, (1975) · Zbl 0293.35041
[7] Maruo, K., On some evolution equations of subdifferential operators, Proc. Japan acad., 51, 304-307, (1975) · Zbl 0328.34060
[8] Kenmochi, N., The semi-discretisation method and nonlinear time-dependent parabolic variational inequalities, Proc. Japan acad., 50, 714-717, (1975) · Zbl 0335.49004
[9] Moreau, J.J., Rétraction d’une multiapplication, Séminaire d’analyse convexe, (1972), Exposé n°13. · Zbl 0353.49033
[10] Peralba, J.C., Un problème d’évolution relatif à un opérateur sous-différentiel dépendant du temps, C.r. acad. sci., Paris, 275, 93-96, (1972) · Zbl 0238.35018
[11] Attouch, H.; Benilan, P.; Damlamian, A.; Picard, C., Inéquations variationnelles d’évolution avec conditions unilatérales, C.r. acad. sci. Paris, 279, 607-609, (1974), Ser. A · Zbl 0309.34049
[12] {\scAttouch} H. & {\scDamlamian} A., Application des méthodes de convexité et de monotonie à l’étude de certaines équations quasi-linéaires, to appear in Proc. R. Soc. Edinburgh. · Zbl 0374.35022
[13] {\scAttouch} H., Mesurabilité et Monotonie, Thése.
[14] Picard, C., Equations d’évolution avec condition unilatérale, Séminaire Lions-brézis, (1973 1974), (Paris VI).
[15] {\scAttouch} H., {\scBenilan} P., {\scDamlamian} A. & {\scPicard} C., Une résolution \( de du/ dt + A(t)u + ∂φ\^{}\{t\}(u)∋⨍\);, to appear.
[16] Brezis, H., Un problème d’évolution avec contraintes unilatérales dépendant du temps, C.r. acad. sci. Paris, 274, 310-312, (1972) · Zbl 0231.35040
[17] {\scRudin} W., Real and Complex Analysis. McGraw Hill.
[18] Damlamian, A., Thesis, (1974), Harvard University
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