Mathematical Sciences: Analytical and Numerical Aspects of Inverse Problems for Differential Equations

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8902532 Vogelius This project has two unrelated parts. One is to derive effective equations for the deformation of plates with rapidly varying composition. The study will focus on optimal bounds for the energies associated with certain models. The other and major part of the project is the study of inverse elliptic problems. The emphasis here is the reconstruction of coefficients in the differential equation from measurements of finitely many parts of Dirichlet and corresponding Neumann data. Numerical algorithms will be developed to implement the reconstruction scheme. The solutions of these inverse problems have application to the imaging of internal nonhomogeneities or tomography. The research on the plate equations is applicable to the optimal design of composite materials.