Inverse Problem for Kinetic Equations
Monday, April 29, 2019 - 3:40pm - 4:30pm
A classical approach in identifying optical parameters in radiative transfer equations is to apply the singular decomposition to their associated Albedo operators. This approach heavily relies on the specific structure of the equation, and thus could be hard to apply to nonlinear equations. In this talk, we show that by making use of classical analytical tools for kinetic equations, we can recover the absorption and scattering coefficients of a class of equations without resorting to fine details of the Albedo operator. Such tools include the maximum principle, energy estimates, and the celebrated averaging lemma. Since our method is largely based on generic properties of kinetic equations, we can apply it to nonlinear equations whose well-posedness in the forward setting is known. This is a joint work with Qin Li.