Structural Stability of Doubly-Nonlinear Flows

Visintin, Augusto

Bollettino dell'Unione Matematica Italiana, Tome 4 (2011), p. 363-391 / Harvested from Biblioteca Digitale Italiana di Matematica

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Résumé

To any maximal monotone operator $\alpha\colon V\to\mathcal{P}(V)$ ( $V$ being a real Banach space),in [MR1009594] S. Fitzpatrick associated a lower semicontinuous and convex function $f\colon V\times V^{\prime}\to\mathbb{R}\cup\{+\infty\}$ such that $f(v,v^{\prime})\geq\langle v^{\prime},v\rangle\quad\forall(v,v^{\prime}),% \qquad f(v,v^{\prime})=\langle v^{\prime},v\rangle\iff v^{\prime}\in\alpha(v).$ On this basis, in this work two classes of doubly-nonlinear evolutionary equations are formulated as minimization principles: $D_{t}\alpha(u)-\operatorname{div}\vec{\gamma}(\nabla u)\ni h,\qquad\alpha(D_{t% }u)-\operatorname{div}\vec{\gamma}(\nabla u)\ni h;$ here $\alpha$ and $\vec{\gamma}$ are maximal monotone mappings, and one of them is assumed to be cyclically monotone. For associated initial- and boundary-value problems, existence of a solution is proved, as well as the stability with respect to variations of the data and of the operators $D_{t}$ , $\nabla$ , $\alpha$ and $\vec{\gamma}$ .

Publié le : 2011-10-01

MR 2906767 | Zbl 1235.35032

@article{BUMI_2011_9_4_3_363_0,
     author = {Augusto Visintin},
     title = {Structural Stability of Doubly-Nonlinear Flows},
     journal = {Bollettino dell'Unione Matematica Italiana},
     volume = {4},
     year = {2011},
     pages = {363-391},
     zbl = {1235.35032},
     mrnumber = {2906767},
     language = {en},
     url = {http://dml.mathdoc.fr/item/BUMI_2011_9_4_3_363_0}
}

Visintin, Augusto. Structural Stability of Doubly-Nonlinear Flows. Bollettino dell'Unione Matematica Italiana, Tome 4 (2011) pp. 363-391. http://gdmltest.u-ga.fr/item/BUMI_2011_9_4_3_363_0/

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