Minimax control of nonlinear evolution equations

摘要

In this paper we study the minimax control of systems governed by a nonlinear, time-dependent evolution inclusion of the subdifferential type. Using some continuity and lower semicontinuity results for the solution map and the cost functional, respectively, we are able to establish the existence of an optimal control. The abstract results are then applied to obstacle problems, semilinear systems with weakly varying coefficients (e.g. oscillating coefficients), and differential variational inequalities.