New variational principles in quasi-static viscoelasticity

A "saddle point" (or maximum-minimum) principle is set up for the quasi-static boundary-value problem in linear viscoelasticity. The appropriate class of convolution-type functionals for it is taken in terms of bilinear forms with a weight function involving Fourier transform. The "minimax" property is shown to hold as a direct consequence of the thermodynamic restrictions on the relaxation function. This approach can be extended to further linear evolution problems where initial data are not prescribed.