Mathematical Sciences: Inverse Problems for Hyperbolic Partial Differential Equations

本项目将解决双曲方程反问题领域的三个问题：非光滑系数方程的正则性根据双特征几何传播的程度，约束优化问题的牛顿型算法的适定性和可计算性，弱凸优化问题解的表征和计算。这里发展的数学将用于根据地震资料确定地球的内部结构。这对于确定自然资源的位置非常有用，而不需要昂贵的钻井。

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.