Simultaneous determination of internal source and coefficients of a diffusion equation from a single boundary measurement

Abstract: In this talk, we will consider the inverse problem of determining simultaneously several class of coefficients and an internal source (a source term or an initial condition) appearing in a diffusion equation from a single boundary measurement. Our problem can be formulated as the simultaneous determination of information about a diffusion process (velocity field, density of the medium) and of the source of diffusion. We consider this problems in the context of a classical diffusion process described by a convection-diffusion equation as well as an anomalous diffusion phenomena described by a time fractional diffusion equation. Some parts of this talk are based on a joint work with Zhiyuan Li, Yikan Liu and Masahiro Yamamoto.

Mathematics

Audience: researchers in the topic

International Zoom Inverse Problems Seminar, UC Irvine