  In a general Hilbert framework, we consider continuous gradient-like
dynamical systems for constrained multiobjective optimization involving
non-smooth convex objective functions. Our approach is in the line of a
previous work where was considered the case of convex di erentiable objective
functions. Based on the Yosida regularization of the subdi erential operators
involved in the system, we obtain the existence of strong global trajectories.
We prove a descent property for each objective function, and the convergence of
trajectories to weak Pareto minima. This approach provides a dynamical
endogenous weighting of the objective functions. Applications are given to
cooperative games, inverse problems, and numerical multiobjective optimization.
