The invariance principle, introduced by LaSalle [40] and subsequentlygeneralized by Hale [34], gives information on the structure of w-limit sets in dynamical systems possessing a Liapunov function, and the principle and related methods have been used to determine the asymptotic behavior of solutions to a wide variety of evolution equations (see Kefs. [4, 10, 17-19, 23-29, 34, 48, 51, 55, 561)....