Mathematical Sciences: Parellel and Distributed Diffusion Models for Heterogeneous Media

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The principal investigator will conduct research developing a fundamental theory for distributed microstructure systems. These systems provide a particularly effective representation of the intricate interface between the components of a composite medium. The qualitative analysis of the solutions of such systems is of significant scientific interest in view of the wide spread application of such systems to physical systems. Reaction-diffusion equations are useful as mathematical models in many areas of engineering, chemistry, and physics. By better understanding the fundamental theory of nonstandard models modelling flows, better numerical predictions of real single phase flow in fractured media will result.