Some results in micromorphic piezoelectricity

This paper deals with the linear theory of micromorphic piezoelectricity. First, the initial boundary value problem is formulated and some uniqueness results are presented. Then, the continuous dependence of solution upon initial data and body loads is investigated. The temporal behavior in terms of the Cesàro means of various parts of the total energy is also studied. The relations describing the asymptotic behavior of mean energies are established by using some Lagrange identities. Finally, the equilibrium theory is considered. In this context, an existence result for weak solutions is established and the effect of a concentrated charge density is studied.