Mathematical Sciences: Inverse Problems for Hyperbolic Partial Differential Equations

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8905878 Symes This project will address three questions in the area of inverse problems for hyperbolic equations: The degree to which regularity propagates according to bicharacteristic geometry for equations with nonsmooth coefficients, the well-posedness and computability via Newton-type algorithms for constrained optimization problems, and the characterization and computation of solutions for weakly convex optimization problems. The mathematics developed here will be used to determine the interior structure of the earth from seismological data. This is very useful in determining the location of natural resources without the expensive boring of wells.