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

8902532 Vogelius这个项目有两个不相关的部分。一是推导具有快速变化成分的板的有效变形方程。研究将集中于与某些模型相关的能量的最优界限。该项目的另一个主要部分是研究逆椭圆问题。这里的重点是从狄利克雷和相应的诺伊曼数据的有限多部分的测量中重建微分方程中的系数。将开发数值算法来实现重建方案。这些反问题的解可应用于内部非均匀性成像或层析成像。对平板方程的研究可用于复合材料的优化设计。

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.