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

• Autores: Santaria Leuyacc, Yony Raúl, Crisostomo Parejas, Jorge Luis
• Formato: artículo
• Fecha de Publicación: 2019
• Institución: Universidad San Ignacio de Loyola
• Repositorio: USIL-Institucional
• Lenguaje: español
• OAI Identifier: oai:repositorio.usil.edu.pe:20.500.14005/8438
• Enlace del recurso: https://hdl.handle.net/20.500.14005/8438; http://onlinelibrary.wiley.com/doi/abs/10.1002/mma.5389; http://dx.doi.org/10.1002/mma.5389
• Nivel de acceso: acceso embargado
• Materia: Dynamical systems; Nonlinear equations; Data storage equipment

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.