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This survey is devoted to the asymptotic behavior of solutions of evolutionequations generated by maximal monotone operators in Hilbert spaces. Theemphasis is in the comparison of the continuous time trajectories to sequencesgenerated by implicit or explicit discrete time schemes. The analysis coversweak convergence for the average process, for the process itself and strongconvergence and aims at highlighting the main ideas and unifying the proofs. Wefurther make the connection with the analysis in terms of almost orbits thatallows for a broader scope.

Evolution equations for maximal monotone operators: asymptotic analysis in continuous and discrete time