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Journal of Convex Analysis 17 (2010), No. 3&4, 1113--1163
Copyright Heldermann Verlag 2010

Evolution Equations for Maximal Monotone Operators: Asymptotic Analysis in Continuous and Discrete Time

Juan Peypouquet
Dep. de Matemática, Universidad Técnica Federico Santa María, Av. España 1680, Valparaíso, Chile

Sylvain Sorin
Faculté de Mathématiques, Université P. et M. Curie - Paris 6, 175 Rue du Chevaleret, 75013 Paris, France

This survey is devoted to the asymptotic behavior of solutions of evolution equations generated by maximal monotone operators in Hilbert spaces. The emphasis is in the comparison of continuous time trajectories to sequences generated by implicit or explicit discrete time schemes. The analysis covers weak convergence for the average process, for the process itself and strong convergence. The aim is to highlight the main ideas and unifying the proofs. Furthermore the connection is made with the analysis in terms of almost orbits that allows for a broader scope.

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