On Parabolic Variational Inequalities with Multivalued Terms and Convex Functionals

In this paper, we consider the following parabolic variational inequality containing a multivalued term and a convex functional: Find u is an element of L-p(0, T; W-0(1, p) (Omega)) and f is an element of F(., ., u) such that u(., 0) = u(0) and < u(t) + Au, v - u > + Psi(v) - Psi(u) >= integral(Q) f(v - u) dx dt for all v is an element of L-p(0, T; W-0(1, p) (Omega)), where A is the principal term; F is a multivalued lower-order term; Psi(u) = integral(T)(0) psi(t, u) dt is a convex functional. Moreover, we study the existence and other properties of solutions of this inequality assuming certain growth conditions on the lower-order term F.