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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4 Citas (Scopus)

Resumen

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.

Idioma originalInglés
Páginas (desde-hasta)871-882
Número de páginas12
PublicaciónMathematical Methods in the Applied Sciences
Volumen42
N.º3
DOI
EstadoPublicada - 1 feb. 2019
Publicado de forma externa

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