bdim: Biblioteca Digitale Italiana di Matematica

Un progetto SIMAI e UMI

Referenza completa

Cannarsa, Piermarco and Da Prato, Giuseppe:
The vanishing viscosity method in infinite dimensions (Il metodo della viscosità artificiale in dimensione infinita)
Atti della Accademia Nazionale dei Lincei. Classe di Scienze Fisiche, Matematiche e Naturali. Rendiconti Serie 8 83 (1989), fasc. n.1, p. 79-84, (English)
pdf (675 Kb), djvu (631 Kb). | MR 1142442 | Zbl 0735.49022

Sunto

Si adatta il metodo della viscosità artificiale al caso infinito dimensionale, dimostrando che la funzione valore di un problema di controllo deterministico si può approssimare con soluzioni di equazioni paraboliche in spazi di Hilbert.
Referenze Bibliografiche
[1] BARBU V. and DA PRATO G., 1983. Solution of the Bellman equation associated with an infinite dimensional Stochastic control problem and synthesis of optimal control. SIAM J. Control Opt., 21, 4: 531-550. | fulltext (doi) | MR 704473 | Zbl 0511.93072
[2] CANNARSA P. and DA PRATO G. Some results on nonlinear optimal control problems and Hamilton-Jacobi equations in infinite dimensions. J. Funct. Anal., (to appear). | fulltext (doi) | MR 1047576 | Zbl 0717.49022
[3] CANNARSA P. and DA PRATO G., 1989. Nonlinear optimal control with infinite horizon for distributed parameter systems and stationary Hamilton-Jacobi equations. SIAM J. Control Opt., 27, 4: 861-875. | fulltext (doi) | MR 1001924 | Zbl 0682.49033
[4] CRANDALL M.G. and LIONS P.L., 1983. Viscosity solutions of Hamilton-Jacobi equations. Trans. Amer. Math. Soc., 277: 183-186. | fulltext (doi) | MR 690039 | Zbl 0469.49023
[5] CRANDALL M.G. and LIONS P.L., 1985. Hamilton-Jacobi equations in infinite dimensions Part I. Uniqueness of Viscosity Solutions. J. Funct. Anal., 62: 379-396. | fulltext (doi) | MR 794776 | Zbl 0627.49013
[6] CRANDALL M.G. and LIONS P.L., 1986. Hamilton-Jacobi equations in infinite dimensions. Part II. Existence of Viscosity Solutions. J. Funct. Anal., 65: 368-405. | fulltext (doi) | MR 826434 | Zbl 0639.49021
[7] CRANDALL M.G. and LIONS P.L., 1986. Hamilton-Jacobi equations in infinte dimensions. Part III. J. Funct. Anal., 68: 368-405. | fulltext (doi) | MR 852660 | Zbl 0639.49021
[8] CRANDALL M.G. and LIONS P.L., 1987. Solutions de visconsitê pour les équations de Hamilton-Jacobi en dimension infinie intervenant dans le contrôle optimal des problèmes d'évolution. C.R. Acad. Sci. Paris, 305: 233-236. | MR 907950
[9] DALECKII J.L., 1966. Differential equations with functional derivatives and stochastic equations for generalized random processes. Dokl. Akad. Nauk SSSR, 166: 1035-1038. | MR 214943
[10] DA PRATO G., 1987. Some Results on Parabolic Evolution Equations with Infinitely Many Variables. J. Differential Equations, 68, 2: 281-297. | fulltext (doi) | MR 892028 | Zbl 0628.35044
[11] DA PRATO G., 1985. Some results on Bellman equation in Hilbert spaces and applications to infinite dimensional control problems. In «Stochastic Differential Systems, Filtering and Control», Lecture Notes in Control and Information Sciences69, Proceedings of the IFIP-WG 7/1 Working Conference, Marseille-Luminy, France, March 12-17, 1984. MATIVIER M. and PARDOUX E. Editors: 270-280.
[12] FLEMING W.H., 1969. The Cauchy problem for a nonlinear first order partial differential equation. J. Differential Equations, 5: 515-530. | fulltext (doi) | MR 235269 | Zbl 0172.13901
[13] GROSS L., 1967. Potential theory in Hilbert space. J. Func. Anal., 1: 123-181. | MR 227747 | Zbl 0165.16403
[14] HAVARNEANU T., 1985. Existence for the Dynamic Programming equations of control diffusion processes in Hilbert spaces. Nonlinear Anal. T.M.A, 9, n° 6: 619-629. | fulltext (doi) | MR 794831 | Zbl 0563.49022
[15] LIONS P.L., 1982. Generalized solutions of Hamilton-Jacobi equations. Pitman, Boston. | Zbl 0497.35001
[16] PIECH M.A., 1969. A Fundamental Solution of the Parabolic Equations in Hilbert spaces. J. Funct. Analysis, 3: 85-114. | MR 251588 | Zbl 0169.47103

La collezione può essere raggiunta anche a partire da EuDML, la biblioteca digitale matematica europea, e da mini-DML, il progetto mini-DML sviluppato e mantenuto dalla cellula Math-Doc di Grenoble.

Per suggerimenti o per segnalare eventuali errori, scrivete a

logo MBACCon il contributo del Ministero per i Beni e le Attività Culturali