Article ID | Journal | Published Year | Pages | File Type |
---|---|---|---|---|
4616112 | Journal of Mathematical Analysis and Applications | 2014 | 15 Pages |
Abstract
We study the asymptotic behavior of parabolic p-Laplacian problems of the form∂uλ∂t(t)−div(Dλ(t)|∇uλ(t)|p−2∇uλ(t))+|uλ(t)|p−2uλ(t)=B(t,uλ(t)) in a bounded smooth domain Ω in RnRn, where n⩾1n⩾1, p>2p>2, Dλ∈L∞([τ,T]×Ω)Dλ∈L∞([τ,T]×Ω) with 0<β⩽Dλ(t,x)⩽M0<β⩽Dλ(t,x)⩽M a.e. in [τ,T]×Ω[τ,T]×Ω, λ∈[0,∞)λ∈[0,∞) and for each λ∈[0,∞)λ∈[0,∞) we have |Dλ(s,x)−Dλ(t,x)|⩽Cλ|s−t|θλ|Dλ(s,x)−Dλ(t,x)|⩽Cλ|s−t|θλ for all x∈Ωx∈Ω, s,t∈[τ,T]s,t∈[τ,T] for some positive constants θλθλ and CλCλ. Moreover, Dλ→Dλ1Dλ→Dλ1 in L∞([τ,T]×Ω)L∞([τ,T]×Ω) as λ→λ1λ→λ1. We prove that for each λ∈[0,∞)λ∈[0,∞) the evolution process of this problem has a pullback attractor and we show that the family of pullback attractors behaves upper semicontinuously at λ1λ1.
Related Topics
Physical Sciences and Engineering
Mathematics
Analysis
Authors
Jacson Simsen, Marcelo J.D. Nascimento, Mariza S. Simsen,