P.D.E.s with hysteresis 30 years later

Augusto Visintin

doi:10.3934/dcdss.2015.8.793

Article Contents

2015, Volume 8, Issue 4: 793-816. Doi: 10.3934/dcdss.2015.8.793

This issue Previous Article Hysteresis operators in metric spaces Next Article

P.D.E.s with hysteresis 30 years later

Augusto Visintin^1,

1.
Dipartimento di Matematica dell'Università degli Studi di Trento, via Sommarive 14, 38123 Povo di Trento

Received: August 31, 2013

Revised: June 30, 2014

Published: July 2015

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Abstract

Continuous and discontinuous hysteresis operators are first reviewed in general. The Duhem model, the generalized play, the (delayed) relay and the Preisach model are outlined, as well as vector extensions of the two latter models.
Two examples of initial- and boundary-value problems for P.D.E.s with hysteresis are then illustrated. Well-posedness is proved for quasilinear parabolic problems with either continuous or discontinuous hysteresis. Existence of a weak solution is shown for second-order quasilinear hyperbolic problems with discontinuous hysteresis.

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Mathematics Subject Classification: 35K60, 35K59, 35L72, 47J40.

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