Upper semicontinuity of global attractors for a viscoelastic equations with nonlinear density and memory effects

Yony Raúl Santaria Leuyacc, Jorge Luis Crisostomo Parejas

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1 Scopus citations

Abstract

© 2018 John Wiley & Sons, Ltd. 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.
Original languageAmerican English
Pages (from-to)871-882
Number of pages12
JournalMathematical Methods in the Applied Sciences
DOIs
StatePublished - 1 Feb 2019

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