A non-autonomous strongly damped wave equation: Existence and continuity of the pullback attractor

作者：Caraballo Tomas^*; Carvalho Alexandre N; Langa Jose A; Rivero Felipe

来源：Nonlinear Analysis-Theory Methods & Applications, 2011, 74(6): 2272-2283.

DOI：10.1016/j.na.2010.11.032

• Non-autonomous damped wave equation
• Existence and structure of the pullback attractor
• Lower and upper semicontinuity

In this paper we consider the strongly damped wave equation with time-dependent terms
u(tt) - Delta u - gamma(t)Delta u(t) + beta(epsilon)(t)u(t) = f(u),
in a bounded domain Omega subset of R(n), under some restrictions on beta(epsilon)(t), gamma(t) and growth restrictions on the nonlinear term f. The function beta(epsilon)(t) depends on a parameter epsilon, beta(epsilon)(t) -> 0. We will prove, under suitable assumptions, local and global well-posedness (using the uniform sectorial operators theory), the existence and regularity of pullback attractors {A(epsilon)(t) : t is an element of R}, uniform bounds for these pullback attractors, characterization of these pullback attractors and their upper and lower semicontinuity at epsilon = 0.

• 出版日期2011-3-15