Visintin: On the Structural Stability of Monotone Flows (Running head: Structural Stability)

Visintin, Augusto:
On the Structural Stability of Monotone Flows (Running head: Structural Stability)
Bollettino dell'Unione Matematica Italiana Serie 9 4 (2011), fasc. n.3, p. 471-479, (English)
pdf (265 Kb), djvu (93 Kb). | MR 2906771 | Zbl 1243.49015

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Flows of the form $D_tu + \alpha(u) \ni h$, with $\alpha$ maximal monotone, are here formulated as null-minimization problems via Fitzpatrick's theory. By means of De Giorgi's notion of $\Gamma$-convergence, we study the compactness and the structural stability of these flows with respect to variations of the source $h$ and of the operator $\alpha$.

Referenze Bibliografiche

[1] A. AMBROSETTI - C. SBORDONE, $\Gamma$-convergenza e G-convergenza per problemi non lineari di tipo ellittico. Boll. Un. Mat. Ital. (5), 13-A (1976), 352-362 | MR 487703 | Zbl 0345.49004

[2] H. ATTOUCH, Variational Convergence for Functions and Operators. Pitman, Boston 1984 | MR 773850 | Zbl 0561.49012

[3] H. BREZIS - I. EKELAND, Un principe variationnel associé à certaines équations paraboliques. I. Le cas indépendant du temps and II. Le cas dépendant du temps. C. R. Acad. Sci. Paris Sér. A-B, 282 (1976), 971-974, and ibid. 1197-1198. | MR 637214 | Zbl 0332.49032

[4] G. DAL MASO, An Introduction to $\Gamma$-Convergence. Birkhäuser, Boston 1993. | fulltext (doi) | MR 1201152 | Zbl 0816.49001

[5] E. DE GIORGI - T. FRANZON, Su un tipo di convergenza variazionale. Atti Accad. Naz. Lincei Rend. Cl. Sci. Fis. Mat. Natur. (8), 58 (1975), 842-850. | MR 448194

[6] S. FITZPATRICK, Representing monotone operators by convex functions. Workshop/Miniconference on Functional Analysis and Optimization (Canberra, 1988), 59-65, Proc. Centre Math. Anal. Austral. Nat. Univ., 20, Austral. Nat. Univ., Canberra, 1988. | MR 1009594 | Zbl 0669.47029

[7] N. GHOUSSOUB, A variational theory for monotone vector fields. J. Fixed Point Theory Appl., 4 (2008), 107-135. | fulltext (doi) | MR 2447965 | Zbl 1177.35093

[8] N. GHOUSSOUB, Selfdual Partial Differential Systems and their Variational Principles. Springer, 2009. | MR 2458698 | Zbl 1357.49004

[9] B. NAYROLES, Deux théorèmes de minimum pour certains systèmes dissipatifs. C. R. Acad. Sci. Paris Sér. A-B, 282 (1976). A1035-A1038. | MR 418609 | Zbl 0345.73037

[10] U. STEFANELLI, The Brezis-Ekeland principle for doubly nonlinear equations. S.I.A.M. J. Control Optim., 8 (2008), 1615-1642. | fulltext (doi) | MR 2425653 | Zbl 1194.35214

[11] L. TARTAR, The General Theory of Homogenization. A Personalized Introduction. Springer, Berlin; UMI, Bologna, 2009. | fulltext (doi) | MR 2582099 | Zbl 1188.35004

[12] A. VISINTIN, Extension of the Brezis-Ekeland-Nayroles principle to monotone operators. Adv. Math. Sci. Appl., 18 (2008), 633-650. | MR 2489147 | Zbl 1191.47067

[13] A. VISINTIN, Scale-transformations of maximal monotone relations in view of homogenization. Boll. Un. Mat. Ital., (9), III (2010), 591-601. | fulltext bdim | fulltext EuDML | MR 2742783

[14] A. VISINTIN, Homogenization of a parabolic model of ferromagnetism. J. Differential Equations, 250 (2011), 1521-1552. | fulltext (doi) | MR 2737216 | Zbl 1213.35066

[15] A. VISINTIN, Structural stability of doubly nonlinear flows. Boll. Un. Mat. Ital., (9), IV (2011) (in press). | fulltext bdim | MR 2906767 | Zbl 1235.35032

[16] A. VISINTIN, Variational formulation and structural stability of monotone equations. (forthcoming). | fulltext (doi) | MR 3044140 | Zbl 1304.47073

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Referenza completa

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Referenze Bibliografiche