<abstract xmlns="http://www.w3.org/1999/xhtml"><p> In this paper, we study the evolution of the energy density of a sequence of solutions of a problem related to a viscoelasticity model where the viscosity term is a pseudo-differential operator of order 2α with α ∈ (0, 1). We calculate the weak limit of the energy density in terms of microlocal defect measures and under special assumption we prove that the viscosity term prevents propagation of concentration and oscillation effects contrary to what happens in the wave equation.</p></abstract>

In this paper, we study the evolution of the energy density of a sequence of solutions of a problem related to a viscoelasticity model where the viscosity term is a pseudo-differential operator of order 2α with α ∈ (0, 1). We calculate the weak limit of the energy density in terms of microlocal defect measures and under special assumption we prove that the viscosity term prevents propagation of concentration and oscillation effects contrary to what happens in the wave equation.

Analysis of the energy decay of a viscoelasticity type equation

Analele ştiinţifice ale Universităţii "Ovidius" Constanţa. Seria Matematică

This work is licensed under the Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 License.

{"article-title":"Analysis of the energy decay of a viscoelasticity type equation"}

In this paper, we study the evolution of the energy density of a sequence of solutions of a problem related to a viscoelasticity model where the viscosity term...

Analysis of the energy decay of a viscoelasticity type equation

Publié en ligne: 21 sept. 2017

Pages: 21 - 45

Reçu: 16 janv. 2016

Accepté: 16 févr. 2016

DOI: https://doi.org/10.1515/auom-2016-0046

Mots clés
viscoelasticity equation, microlocal defect measures, energy density.

© 2017

This work is licensed under the Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 License.

Analysis of the energy decay of a viscoelasticity type equation

Publié en ligne: 21 sept. 2017

Pages: 21 - 45

Reçu: 16 janv. 2016

Accepté: 16 févr. 2016

DOI: https://doi.org/10.1515/auom-2016-0046

Mots clésviscoelasticity equation, microlocal defect measures, energy density.

© 2017

This work is licensed under the Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 License.

Mots clés
viscoelasticity equation, microlocal defect measures, energy density.