MATH Seminar

Title: Inverse problems for nonlinear hyperbolic equations
Colloquium: Analysis and Differential Geometry
Speaker: Yiran Wang of Stanford University
Contact: David Borthwick, dborthw@emory.edu
Date: 2019-02-21 at 4:00PM
Venue: MSC W303
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Abstract: We consider the inverse problem of determining coefficients of nonlinear hyperbolic equations from measurements of wave responses. The problem has wide applications for example in general relativity (the Einstein equations) and seismology (the elastic wave equations). It is known that the nonlinear interaction of waves could generate new responses and such interactions have been studied using plane waves in the literature. In this talk, we analyze the nonlinear response and give a precise characterization using microlocal methods, and show how nonlinearity helps us to solve the inverse problem.