Mathematical Sciences: Parallel and Distributed Diffusion Models for Heterogeneous Media

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DMS-9500920 Showalter Mathematical models of diffusion in heterogeneous media will be developed as nonlinear systems of partial differential equations. These diffusion processes include examples of diffusion through porous or fissured media (with saturation, absorption, or phase change) and conduction through composite semiconductor materials. The singular or degenerate nature of these systems arise from material properties and from the geometry of the composition. Major objectives include the development by homogenization theory of two-scale models, proof of well-posedness results in appropriate function spaces, and the investigation of properties of solutions for the various systems. Mathematical models of diffusion in composite media will be developed. These diffusion processes include examples of heat conduction (with solid - liquid phase change), diffusion of fluid through porous or fissured media (with saturation), absorption by granulated substance, and the macroscopic description of current flow in semi-conductor materials. The singular or degenerate nature of these systems arise from properties of the materials and from the geometry of the composition. Major objectives include the development of exact small-scale models to describe the flow across the intricate interface between the components of the media and averaged large-scale models which are necessary for the computation of solutions.