An existence theorem for the magneto-viscoelastic problem

Sandra Carillo; Vanda Valente; Giorgio Vergara Caffarelli

doi:10.3934/dcdss.2012.5.435

Article Contents

2012, Volume 5, Issue 3: 435-447. Doi: 10.3934/dcdss.2012.5.435

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An existence theorem for the magneto-viscoelastic problem

1.
Dipartimento di Scienze di Base e Applicate per l’Ingegneria, sez. matematica – 16, Via A. Scarpa, SAPIENZA Università di Roma, Rome, 00161
2.
Istituto per le Applicazioni del Calcolo “Mauro Picone”, Consiglio Nazionale delle Ricerche, Via dei Taurini 19, Rome, 00185

Received: August 2010

Revised: September 2010

Published: June 2012

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Abstract

The dynamics of magneto-viscoelastic materials is described by a nonlinear system which couples the equation of the magnetization, given in Gibert form, and the viscoelastic integro-differential equation for the displacements. We study the general three-dimensional case and establish a theorem for the existence of weak solutions. The existence is proved by compactness of the approximated penalty problem.

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Mathematics Subject Classification: Primary: 74H20, 35Q74; Secondary: 45K05.

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