Asymptotic behavior of solutions to certain nonlinear parabolic evolution equations. II (Q1202218)

The purpose of this paper is to show that given a pair of solutions \(u_ 1\), \(u_ 2\) in \(W^ 1_{\text{loc}}((0,\infty);H)\) of the time- dependent evolution equation \[ (d/dt)u(t)+ \partial \psi^ t(u(t))\ni 0,\qquad\text{a.e. }t\geq 0,\tag{1.1} \] the strong convergence \[ s- \lim_{t\to\infty} \{u_ 1(t)- u_ 2(t)\}=\text{const.}\in H\tag{1.2} \] is valid, where \(H\) is a real Hilbert space, and for each \(t\in [0,\infty)\), \(\psi^ t\) is a proper lower semi-continuous (l.s.c.) convex functional defined in \(H\) and \(\partial\psi^ t\) denotes the subdifferential of \(\psi^ t\). [For part I see ibid. 14, 265-281 (1984; Zbl 0599.47105)].