info:eu-repo/semantics/article
Upper semicontinuity of global attractors for a viscoelastic equations with nonlinear density and memory effects
Fecha
2019-02Registro en:
Santaria Leuyacc, Y. R., & Crisostomo Parejas, J. L. (2019). Upper semicontinuity of global attractors for a viscoelastic equations with nonlinear density and memory effects. Mathematical Methods in the Applied Sciences, 42(3), 871-882.
10.1002/mma.5389
0170-4214
Mathematical Methods in the Applied Sciences
Autor
Santaria Leuyacc, Yony Raúl
Crisostomo Parejas, Jorge Luis
Institución
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.