HIGH FREQUENCY ANALYSIS OF FAMILIES OF SOLUTIONS TO THE EQUATION OF VISCOELASTICITY OF KELVIN–VOIGT

Author:

ATALLAH-BARAKET AMEL1,FERMANIAN KAMMERER CLOTILDE2

Affiliation:

1. Faculté des Sciences de Tunis, Dpt. de Mathématiques, 1060, Tunis, Tunisie

2. Université de Cergy-Pontoise, Mathématiques, 2 avenue Adolphe Chauvin, BP 222, Pontoise, 95 302 Cergy-Pontoise cedex, France

Abstract

In this paper, we study the evolution of the energy density of a sequence of solutions to the Kelvin–Voigt viscoelasticity equation. We do not suppose lower bounds on the non-negative viscosity matrix. We prove that, in the zone where the viscosity matrix is invertible, this term prevents propagation of concentation and oscillation effects contrary to what happens in the wave equation. We calculate precisely the weak limit of the energy density in terms of microlocal defect measures associated with the initial data under the assumption that the oscillations of the data are not microlocally localized on directions which are in the kernel of the viscosity matrix.

Publisher

World Scientific Pub Co Pte Lt

Subject

General Mathematics,Analysis

Reference12 articles.

1. Mesures de défaut de compacité, application au système de Lamé

2. C. Do, Variational Methods in the Mechanics of Solids, ed. S. Nemat Nasser (Pergamon Press, 1978) pp. 237–241.

3. Oscillations and Energy Densities in the Wave Equation

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