Global solutions to a coupled parabolic-hyperbolic system with hysteresis in 1-d magnetoelasticity
- Krejčí, Pavel
- Sprekels, Jürgen
2010 Mathematics Subject Classification
- 35G25 73R05 82D40.
- Magnetic hysteresis, ferromagnetism, Preisach operator, magnetoelasticity, PDE's with hysteresis, parabolic-hyperbolic systems
In this paper the system of field equations governing the one-dimensional magnetoelastic evolution in a ferromagnet, which is immersed in an electromagnetic field and subjected to mechanical loads at a constant temperature below the Curie point, is considered. It is assumed that displacement currents are negligible and that all field quantities depend on one space variable only. The hysteretic relation between the applied magnetic field and the magnetization in the ferromagnet are modeled using the notion of hysteresis operators; in particular, hysteresis operators of Preisach type are included. It is shown that an initial-boundary value problem for the system admits global solutions for arbitrary initial data, if viscosity is present in the material, and for small initial data, if not. The considered field equations may be regarded as a model for the effect of magnetostriction in ferromagnets.
- Nonlin. Anal., 33 (1998), pp. 341-358