  This paper addresses a doubly nonlinear parabolic inclusion of the form
$A(u_t)+B(u)\ni f$. Existence of a solution is proved under suitable
monotonicity, coercivity, and structure assumptions on the operators $A$ and
$B$, which in particular are both supposed to be subdifferentials of
functionals on $L^2(\Omega)$. Moreover, under additional hypotheses on $B$,
uniqueness of the solution is proved. Finally, a characterization of
$\omega$-limit sets of solutions is given and we investigate the convergence of
trajectories to limit points.
