Stability and uniqueness in double porosity elasticity

We study a model for anisotropic linear elastodynamics which allows for the body to have a doubly porous structure. A macro porosity connected to pores in the body and a micro porosity which reflects fissures in the porous skeleton. The elastic coefficients are required only to possess a symmetry and not be sign – definite. We show by introducing a novel functional that the solution to the boundary – initial value problem for this material is unique. By modifying this functional we show how to obtain Hölder stability estimates for the solution.