This paper is devoted to showing the upper semicontinuity of global attractors associated with the family of nonlinear viscoelastic equations |∂tu|ρ∂ttu−Δ∂ttu−Δu+∫0+∞μ(s)Δu(t−s)ds+f(u)=h, in a three‐dimensional space, for f gro...
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https://www.riss.kr/link?id=O119771580
2019년
-
0170-4214
1099-1476
SCIE;SCOPUS
학술저널
871-882 [※수록면이 p5 이하이면, Review, Columns, Editor's Note, Abstract 등일 경우가 있습니다.]
0
상세조회0
다운로드다국어 초록 (Multilingual Abstract)
This paper is devoted to showing the upper semicontinuity of global attractors associated with the family of nonlinear viscoelastic equations |∂tu|ρ∂ttu−Δ∂ttu−Δu+∫0+∞μ(s)Δu(t−s)ds+f(u)=h, in a three‐dimensional space, for f gro...
This paper is devoted to showing the upper semicontinuity of global attractors associated with the family of nonlinear viscoelastic equations
|∂tu|ρ∂ttu−Δ∂ttu−Δu+∫0+∞μ(s)Δu(t−s)ds+f(u)=h,
in a three‐dimensional space, for f growing up to the critical exponent and dependent on ρ ∈ [0,4), as ρ→0+. This equation models extensional vibrations of thin rods with nonlinear material density ϱ(∂tu) = |∂tu|ρ and presence of memory effects. This type of problems has been extensively studied by several authors; the existence of a global attractor with optimal regularity for each ρ ∈ [0,4) were established only recently. The proof involves the optimal regularity of the attractors combined with Hausdorff's measure.
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