Source and coefficient identification problems for the wave equation on graphs

Abstract

Avdonin and Kurasov proposed a leaf peeling method based on the boundary control to recover a potential for the wave equation on a tree. Avdonin and Nicaise considered a source identification problem for the wave equation on a tree. This paper extends the methodology to the wave equation with unknown potential and source distributed parameters defined on a general tree graph.

Leaf Peeling method for the wave equation on metric tree graphs

“…In [8] inverse dynamical, spectral and scattering problems for the Schrödinger equation on quantum trees were studied and the leaf peeling (LP) was proposed. This method was extended to boundary inverse problems for various types of PDEs on trees and various matching conditions in a series of subsequent papers ( [9,10,4,7,6,5]). The LP method allows one to recover not only coefficients in the equations on the graphs edges but also the lengths of the edges and topology (connectivity) of the graph.…”