Local H\"older stabilities for inverse problems of first-order hyperbolic equations

TL;DR

This paper establishes local H"older stability estimates for inverse problems involving first-order hyperbolic equations with time-dependent coefficients, using Carleman estimates to analyze the stability of source and coefficient reconstructions.

Contribution

The paper introduces new local H"older stability results for inverse problems of first-order hyperbolic equations with time-dependent coefficients, employing Carleman estimates.

Findings

Established local H"older stability for inverse source problems.

Proved local H"older stability for inverse coefficient problems.

Applied Carleman estimates to derive stability results.

Abstract

In this paper, we consider a Cauchy problem for a first-order hyperbolic equation with time-dependent coefficients. Cauchy data are given on a lateral subboundary and we obtain local H\"older stabilities for inverse source and coefficient problems via a Carleman estimate.