Quasistatic evolution of magnetoelastic plates via dimension reduction

Martin Kružík; Ulisse Stefanelli; Chiara Zanini

doi:10.3934/dcds.2015.35.5999

Article Contents

2015, Volume 35, Issue 12: 5999-6013. Doi: 10.3934/dcds.2015.35.5999

This issue Previous Article Schauder estimates for solutions of linear parabolic integro-differential equations Next Article Characterization of function spaces via low regularity mollifiers

Quasistatic evolution of magnetoelastic plates via dimension reduction

1.
Institute of Information Theory and Automation of the ASCR, Pod vodárenskou věží 4, 182 08 Prague
2.
Faculty of Mathematics, University of Vienna, Oskar-Morgenstern-Platz 1, A-1090 Vienna
3.
Dipartimento di Matematica, Politecnico di Torino, Corso Duca degli Abruzzi 24, 10129 Torino

Received: May 2014

Published: December 2015

Abstract / Introduction Related Papers Cited by

Abstract

A rate-independent model for the quasistatic evolution of a magnetoelastic plate is advanced and analyzed. Starting from the three-dimensional setting, we present an evolutionary $\Gamma$-convergence argument in order to pass to the limit in one of the material dimensions. By taking into account both conservative and dissipative actions, a nonlinear evolution system of rate-independent type is obtained. The existence of so-called energetic solutions to such system is proved via approximation.

Keywords:

Magnetoelasticity,
energetic solution,
existence,
dimension reduction,
$\Gamma$-convergence for rate-independent processes.

Mathematics Subject Classification: Primary: 74F15, 74N30, 35K55.

Citation:

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