Inverse problems for nonlinear hyperbolic equations
Dr. Yiran Wang
Department of Mathematics
Stanford University
ABSTRACT: We consider the inverse problem of determining coefficients of nonlinear hyperbolic equations from the measurements of wave responses, which has wide applications for example in general relativity (the Einstein equations) and seismology (elastic systems). The problem we consider cannot be solved by linearization. It is observed that the nonlinear interactions of waves could generate new responses. In this talk, we will give precise characterizations of such nonlinear responses using microlocal analysis and show how they can be used to solve the inverse problem.
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