Upper semicontinuity of global attractors for a viscoelastic equations with nonlinear density and memory effects
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John Wiley and Sons Ltd
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2019-02
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Santaria Leuyacc, Y. R., & Crisostomo Parejas, J. L. (2019). Upper semicontinuity of global attractors for a viscoelastic equations with nonlinear density and memory effects. Mathematical Methods in the Applied Sciences, 42(3), 871-882.
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Mathematical Methods in the Applied Sciences
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This paper is devoted to showing the upper semicontinuity of global attractors associated with the family of nonlinear viscoelastic equations (Formula presented.) 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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0170-4214