Gleanings from magneto-viscoelasticity problems

An overview on existence and/or uniqueness results concerning magneto-viscoelasticity models is presented. The coupling of the viscoelastic behaviour of the material under investigation with effects of magnetisation is considered. The first one is modelled via a linear integro-differential equation to take into account the memory of the deformation behaviour of the viscoelastic material. Conversely, a nonlinear differential equation is considered to describe the action of an external magnetic field. The coupling of these two different effects is of interest in describing the mechanical response of new materials. The attention is focussed on the relaxation modulus: the kernel in the viscoelastic model. In [1] and [2] the usual regularity assumptions, which originate from thermodynamics, are adopted; hence, the kernel in the integro-differential equation is regular. These as- sumptions are modified in the subsequent [3] and [4] where, respectively, the linear and nonlinear problems are studied in the case of a kernel an unbounded at the origin.