Quasilinear parabolic variational inequalities with multi-valued lower-order terms (Q2253928)

This paper is concerned with the study of the mathematical theory for parabolic variational inequalities with upper semicontinuous multi-valued functions and provides not only existence results but also useful comparison and enclosure principles as well as a qualitative study of the solution sets. The paper deals with the coercive case, where the existence of solutions follows from penalty arguments and the solvability of equations with multi-valued pseudomonotone operators, and with the noncoercive case, where such a growth condition is not assumed. The authors establish a sub-supersolution method that allows to prove existence, comparison and enclosure results.