Γ-compactness and Γ-stability of maximal monotone flows

Abstract

The compactness and the stability of the weak solution of nonautonomous maximal monotone flows are proved with respect to nonparametric perturbations of the operator. To this purpose the flow is formulated in weak form as a null-minimization problem, and De Giorgi's notion of Γ-convergence is used. It is proved that all sequences of those flows have a Γ-convergent subsequence, and that the Γ-limit is also a maximal monotone flow and exhibits no long memory. These results can be applied to several quasilinear equations.