A class of evolution variational inequalities with nonconvex constraints.

We study a nonconvex constrained evolution problem for a set being the union of a finite number of convex sets. The problem generalizes the classical parabolic variational inequality of the second kind and contains an operator of L- -type. The existence result for this problem is proved using a variational-hemivariational inequality approach, a surjectivity theorem for multivalued pseudomonotone operators in a reflexive Banach space and a penalization method in which a small parameter does not have to tend to zero. [ABSTRACT FROM AUTHOR]