The sensitivity of parametric evolution inclusions generated by time dependent convex subdifferentials (Q1900416)

The following family of evolution equations defined on a Hilbert space is considered: \[ - x_n'(t)\in \partial\phi^t_n(x_n(t))+ F_n(t, x_n(t)),\quad x_n(0)= x_{0n}. \] Assuming that the subdifferential operators converge in the resolvent sense (i.e. \(\lim_{n\to +\infty}(I+ \lambda\partial\phi^t_n)^{- 1}x\to (I+ \lambda\partial\phi^t)^{- 1} x)\) and the multivalued perturbations \(F_n\) converge to \(F\) with respect to Hausdorff distance it is proved that the solution sets of the above inclusions do converge in the Kuratowski sense to the solution set of the ``limiting'' inclusion \[ - x'(t)\in \partial\phi^t(x(t))+ F(t, x(t)),\quad x_n(0)= x_0. \] An example of a multivalued parabolic boundary value problem is given.