Optimal Runge approximation for damped nonlocal wave equations and simultaneous determination results

TL;DR

This paper develops an optimal Runge approximation theorem for damped nonlocal wave equations, enabling new uniqueness results in inverse problems and simultaneous parameter determination in both linear and semilinear cases.

Contribution

It extends the theory of very weak solutions to nonlocal wave equations and establishes an optimal Runge approximation theorem for the first time.

Findings

Proves new uniqueness results for inverse problems

Establishes an optimal Runge approximation theorem

Enables simultaneous determination in linear and semilinear regimes

Abstract

The main purpose of this article is to establish new uniqueness results for Calder\'on type inverse problems related to damped nonlocal wave equations. To achieve this goal we extend the theory of very weak solutions to our setting, which allows to deduce an optimal Runge approximation theorem. With this result at our disposal, we can prove simultaneous determination results in the linear and semilinear regime.