We study the existence of quasivariational and variational solutions to a class of nonlinear evolution systems in convex sets of Banach spaces describing constraints on a linear combination of partial derivatives of the solutions. The quasilinear operators are of monotone type, but are not required to be coercive for the existence of weak solutions, which is obtained by a double penalization/regularization for the approximation of the solutions. In the case of timedependent convex sets that are independent of the solution, we also show the uniqueness and the continuous dependence of the strong solutions of the variational inequalities, extending previous results to a more general framework. (Joint work with Fernando Miranda and José Francisco Rodrigues)
