# American Institute of Mathematical Sciences

June  2012, 5(3): 435-447. doi: 10.3934/dcdss.2012.5.435

## 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, Italy, Italy 2 Istituto per le Applicazioni del Calcolo “Mauro Picone”, Consiglio Nazionale delle Ricerche, Via dei Taurini 19, Rome, 00185, Italy

Received  August 2010 Revised  September 2010 Published  October 2011

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.
Citation: Sandra Carillo, Vanda Valente, Giorgio Vergara Caffarelli. An existence theorem for the magneto-viscoelastic problem. Discrete & Continuous Dynamical Systems - S, 2012, 5 (3) : 435-447. doi: 10.3934/dcdss.2012.5.435
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