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

Santaria Leuyacc, Yony Raúl; Crisostomo Parejas, Jorge Luis · Universidad San Ignacio de Loyola (2019) · DOI: 10.1002/mma.5389

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.

Instituciones: Universidad San Ignacio de Loyola