On the basis of this project the following six mathematical models will be presented and the non-classical problems of steady vibrations of these models will be extensively investigated:

a) The 3D linear mathematical models of the MGT thermoelasticity and thermoviscoelasticity for porous materials based on Darcy’s law;

b) The 3D linear mathematical models of the MGT thermoelasticity and thermoviscoelasticity for porous materials based on the volume fraction concept;

c) The 3D coupled linear mathematical models of the MGT thermoelasticity and thermoviscoelasticity for porous materials based on the combination of Darcy’s law and the volume fraction concept.

    In each theory, the basic equations of dynamics and steady vibrations will be obtained. The fundamental solutions of the systems of steady vibration equations of these theories will be constructed by means of elementary functions. Basic properties of surface and volume potentials will be established. The existence and uniqueness theorems of solutions of internal and external boundary value problems of steady vibrations will be proved.     

  These new models of the MGT thermoelasticity and thermoviscoelasticity will be more complicated that the earlier proposed models of thermoelasticity and thermoviscoelasticity for porous media. In addition, on the basis of this project the new non-classical boundary value problems of steady vibrations of the above mentioned linear mathematical models of the MGT thermoelasticity will be completely investigated by using the potential method and the theory of singular integral equations.