Uniqueness and Stability by Energy Methods

Abstract

In this chapter we investigate questions of uniqueness, continuous dependence on the initial data, and continuous dependence on the model itself, by employing techniques based on the energy function generated by the system of equations. We concentrate on equations of elasticity with a double porosity structure, or thermoelasticity with a double porosity structure. We firstly deal with a thermoelastic body with a double porosity structure allowing for cross inertia coefficients, equations (2.33), when the body is bounded. After that we examine the equations for isothermal elasticity with double porosity, equations (2.25), (2.26) and (2.27), when the domainΩ is unbounded.