Well-posedness and long-time behaviour for a class of doubly nonlinear equations

This paper addresses a doubly nonlinear inclusion of parabolic type. Existence of a solution is proved under suitable monotonicity, coercivity, and structure assumptions on the (possibly nonlinear) operators governing the inclusion, which are supposed to be of subdifferential type. Under additional hypotheses, uniqueness of the solution is also proved. Finally, a characterization of omega-limit sets of solutions is given and the convergence of trajectories to limit points is analyzed.