Existence for implicit differential equations in Banach spaces
Barbu, Viorel ; Favini, Angelo
Atti della Accademia Nazionale dei Lincei. Classe di Scienze Fisiche, Matematiche e Naturali. Rendiconti Lincei. Matematica e Applicazioni, Tome 3 (1992), p. 203-215 / Harvested from Biblioteca Digitale Italiana di Matematica

We prove two existence results on abstract differential equations of the type dBu/dt+Au=f and we give some applications of them to partial differential equations.

Si dimostrano due risultati di esistenza per equazioni differenziali astratte del tipo dBu/dt+Au=f e si danno alcune applicazioni di essi ad equazioni alle derivate parziali.

Publié le : 1992-09-01
@article{RLIN_1992_9_3_3_203_0,
     author = {Viorel Barbu and Angelo Favini},
     title = {Existence for implicit differential equations in Banach spaces},
     journal = {Atti della Accademia Nazionale dei Lincei. Classe di Scienze Fisiche, Matematiche e Naturali. Rendiconti Lincei. Matematica e Applicazioni},
     volume = {3},
     year = {1992},
     pages = {203-215},
     zbl = {0765.34043},
     mrnumber = {1186916},
     language = {en},
     url = {http://dml.mathdoc.fr/item/RLIN_1992_9_3_3_203_0}
}
Barbu, Viorel; Favini, Angelo. Existence for implicit differential equations in Banach spaces. Atti della Accademia Nazionale dei Lincei. Classe di Scienze Fisiche, Matematiche e Naturali. Rendiconti Lincei. Matematica e Applicazioni, Tome 3 (1992) pp. 203-215. http://gdmltest.u-ga.fr/item/RLIN_1992_9_3_3_203_0/

[1] Amirat, Y., Ecoulements en milieu poreux n'obéissant pas à la loi de d'Arcy. Mathematical Modelling and Numer. Anal., 25, n. 3, 1991, 273-306. | MR 1103090 | Zbl 0727.76106

[2] Barbu, V., Nonlinear Semigroups and Differential Equations in Banach Spaces. Nordhoff, Leyden1976. | MR 390843 | Zbl 0328.47035

[3] Barbu, V., Existence for nonlinear Volterra equations in Hilbert Spaces. SIAM J. Math. Anal., 10, 1979, 552-569. | MR 529073 | Zbl 0462.45021

[4] Barbu, V., Degenerate nonlinear Volterra integral equations in Hilbert spaces. In: S. Londen - O. Staffans (eds.), Volterra Equations. Lecture Notes in Mathematics, vol. 737, Springer Verlag, 1979, 2-23. | MR 551024 | Zbl 0462.45022

[5] Berger, M. S., Nonlinearity and Functional Analysis. Academic Press, New York1977. | MR 488101 | Zbl 0368.47001

[6] Bernis, F., Existence results for doubly nonlinear higher order parabolic equations on unbounded domains. Math. Ann., 279, 1988, 373-393. | MR 922422 | Zbl 0609.35048

[7] Blanchard, D. - Francfort, G. A., A few results on a class of degenerate parabolic equations. Ann. Scuola Normale Sup. Pisa, 18, 1991, 213-249. | MR 1129302 | Zbl 0778.35046

[8] Brezis, H., Intégrales convexes dans les espaces de Sobolev. Israel J. Math., 13, 1972, 9-23. | MR 341077 | Zbl 0249.46017

[9] Colli, P. - Visinttn, A., On a class of doubly nonlinear evolution equations. Comm. Partial Diff. Eqs., 15 (5), 1990, 737-756. | MR 1070845 | Zbl 0707.34053

[10] Da Prato, G. - Grisvard, P., Sommes d'operateurs linéaires et équations différentielles opérationnelles. J. Math. Pures Appl., 54, 1975, 305-387. | MR 442749 | Zbl 0315.47009

[11] Di Benedetto, E. - Showalter, R. E., Implicit degenerate equations and applications. SIAM J. Math. Anal., 12, 1981, 731-751. | MR 625829 | Zbl 0477.47037

[12] Favini, A., Abstract potential operators and spectral methods for a class of degenerate evolution problems. J. Diff. Eqs., 39, 1981, 212-225. | MR 607782 | Zbl 0422.34025

[13] Favini, A. - Yagi, A., Multivalued linear operators and degenerate evolution equations. Annali di Mat. Pura Appl., to appear. | MR 1219605 | Zbl 0786.47037

[14] Grange, O. - Mignot, F., Sur la résolution d'une équation et d'une inequation parabolique non-linéaire. J. Funct. Anal., 11, 1972, 77-92. | MR 350207 | Zbl 0251.35055

[15] Showalter, R. E. - Walkington, N. J., A diffusion system for fluid in fractured media. Diff. and Integral Eqs., 3, 1990, 219-236. | MR 1025175 | Zbl 0753.35045