Inverse problems for the damped wave equations

We consider wave equations of Westervelt type arising from acoustic imaging. In our linear local model, our goal is to determine the metric up to an isometry from the knowledge of the source-to-solution map, and our approach relies on the Laplace transform and the inverse spectral theory. In our nonlinear fractional model, our goal is to determine the coefficient of the nonlinearity from the knowledge of the source-to-solution map, and our approach relies on the unique continuation and the multiple-fold linearization. This is a joint work with Dr. Yang Zhang.