An inverse problem for semilinear wave equations on metric tree graphs

TL;DR

This paper addresses an inverse problem for semilinear wave equations on metric tree graphs, aiming to recover the graph's structure, edge lengths, potential, and nonlinear coefficient from boundary data.

Contribution

It introduces a method to uniquely determine the graph's connectivity, edge lengths, potential, and nonlinear coefficient using boundary measurements.

Findings

Successfully reconstructs graph structure and parameters from boundary data

Provides a theoretical framework for inverse problems on metric graphs

Extends inverse problem techniques to nonlinear wave equations

Abstract

We study the inverse problem for a semilinear wave equation on metric tree graphs. From the Dirichlet-to-Neumann map defined at all but one of the boundary vertices, we recover unknown connectivity of the graph, lengths of the edges, the time-independent potential and the time-dependent coefficient of the nonlinear term of the equation.