A class of evolution variational inequalities with nonconvex constraints. (3rd October 2019) - Peng, Zijia; Gasiński, Leszek; Migórski, Stanisław; Ochal, Anna
ABSTRACT: 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 - ( S ) + -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.