Asymptotically autonomous multivalued Cauchy problems with spatially variable exponents

JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS

卷:445

Article

Kloeden, Peter E.¹  Simsen, Jacson^2,3  Simsen, Mariza Stefanello^2,3 

[1] Huazhong Univ Sci & Technol, Sch Math & Stat, Wuhan 430074, Peoples R China

[2] Univ Fed Itajuba, Inst Matemat & Computacao, Av BPS 1303, BR-37500903 Itajuba, MG, Brazil

[3] Univ Duisburg Essen, Fak Math, Thea Leymann Str 9, D-45127 Essen, Germany

关键词: Multivalued Cauchy problem;    Variable exponents;    Pullback attractors;    Time-dependent operator;    Asymptotically autonomous inclusion;   

DOI  :  10.1016/j.jmaa.2016.08.004

来源: Elsevier

【 摘 要 】

We study the asymptotic behavior of a non-autonomous multivalued Cauchy problem of the form partial derivative u/partial derivative t(t) - div(D(t)vertical bar del u(t)vertical bar(p(x)-2)del u(t)) + vertical bar u(t)vertical bar(p(x)-2)u(t) + F(t, u(t)) (sic) 0 on a bounded smooth domain Omega in R-n >= 1 with a homogeneous Neumann boundary condition, where the exponent p(.) is an element of C((Omega) over bar) satisfies p- := min p(x) > 2. We prove the existence of a pullback attractor and study the asymptotic upper semicontinuity of the elements of the pullback attractor U = {A(t) : t is an element of R} as t -> infinity for the non -autonomous evolution inclusion in a Hilbert space H under the assumptions, amongst others, that F is a measurable multifunction and D is an element of L-infinity([tau,T] x Omega) is bounded above and below and is monotonically nonincreasing in time. The global existence of solutions is obtained through results of Papageorgiou and Papalini. (C) 2016 Elsevier Inc. All rights reserved.

【 授权许可】

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