1. Upper semicontinuity of global attractors for a viscoelastic equations with nonlinear density and memory effects
- Author
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Yony Raúl Santaria Leuyacc and Jorge Luis Crisostomo Parejas
- Subjects
Thesaurus (information retrieval) ,Dynamical systems theory ,General Mathematics ,010102 general mathematics ,General Engineering ,Nonlinear equations ,01 natural sciences ,Viscoelasticity ,010101 applied mathematics ,Nonlinear system ,Data storage equipment ,Attractor ,Dynamical systems ,Applied mathematics ,0101 mathematics ,Mathematics - Abstract
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. Revisado por pares
- Published
- 2019