Hyperbolic system of balance laws modeling dissipative ionic crystals

Abstract.

Based on the classical continuum theory of electroelasticity which includes polarization gradients as independent variables, we propose a constitutive model for ionic crystals accounting for both ionic and electronic contributions to polarization. Dissipation is modeled via internal variables which satisfy suitable evolution equations and the consequences of the second law of thermodynamics are exploited to cast the non-linear problem in the form of a symmetric hyperbolic system of balance laws. The stability of perturbations with respect to unstrained, unpolarized states is discussed. A set of linear equations is also derived for the fully electromagnetic problem which generalizes previous results.