Nonlinear inverse problem for identifying a coefficient of the lowest term in hyperbolic equation with nonlocal conditions

TL;DR

This paper addresses a nonlinear inverse boundary value problem for a hyperbolic equation with nonlocal conditions, establishing existence and uniqueness of solutions using Fourier methods and contraction mappings.

Contribution

It introduces an auxiliary inverse problem and proves its equivalence to the original, providing new theoretical results for inverse coefficient problems in hyperbolic equations.

Findings

Proved equivalence between auxiliary and original inverse problems.

Established existence and uniqueness of solutions for smaller time values.

Applied Fourier method and contraction mapping principle successfully.

Abstract

In this paper, a nonlinear inverse boundary value problem for the second-order hyperbolic equation with nonlocal conditions is studied. To investigate the solvability of the original problem, we first consider an auxiliary inverse boundary value problem and prove its equivalence (in a certain sense) to the original problem. Then using the Fourier method and contraction map pings principle, the existence and uniqueness theorem for auxiliary problem is proved. Further, on the basis of the equivalency of these problems the existence and uniqueness theorem for the classical solution of the considered inverse coefficient problem is proved for the smaller value of time.