We consider inverse problems concerning the one-dimensional viscous Burgers equation and some related nonlinear systems (involving heat effects, variable density, and fluid-solid interaction). We are dealing with inverse problems in which the goal is to find the size of the spatial interval from some appropriate boundary observations. Depending on the properties of the initial and boundary data, we prove uniqueness and non-uniqueness results.  Moreover, we also solve these inverse problems numerically and computing approximations of the interval sizes.

This is a joint work with Jone Apraiz (University of Basque Country), Enrique Fernández-Cara (University of Sevilla and IMUS) and Masahiro Yamamoto (University of Tokyo).

Zoom meeting: Link