刊名:Journal of Mathematical Analysis and Applications
出版年:2017
出版时间:1 January 2017
年:2017
卷:445
期:1
页码:513-531
全文大小:414 K
文摘
We study the asymptotic behavior of a non-autonomous multivalued Cauchy problem of the form
on a bounded smooth domain Ω in Rn, n≥1 with a homogeneous Neumann boundary condition, where the exponent satisfies p− := minp(x)>2. We prove the existence of a pullback attractor and study the asymptotic upper semicontinuity of the elements of the pullback attractor A={A(t):t∈R} as t→∞ for the non-autonomous evolution inclusion in a Hilbert space H under the assumptions, amongst others, that F is a measurable multifunction and D∈L∞([τ,T]×Ω) is bounded above and below and is monotonically nonincreasing in time. The global existence of solutions is obtained through results of Papageorgiou and Papalini.