Work

Uniqueness in determining multidimensional domains with unknown initial data

Year: 2026

Type: article

Abstract: This paper addresses several geometric inverse problems for linear parabolic systems where the initial data (and sometimes also the coefficients of the equations) are unknown. The goal is to identify a subdomain within a multidimensional set. The nonhomogeneous part of the equation is expressed as a function satisfying some specific assumptions near a positive time. We establish uniqueness results by incorporating observations that can be on either a part of the boundary or in an interior (small) domain. Through this process, we also get information concerning the initial data. The main tools required for the proofs include semigroup theory, unique continuation and time analyticity results.

Source: Inverse Problems

DOI: 10.1088/1361-6420/ae9e68

Authors: J Apraiz, A Doubova, E Fernández-Cara, M Yamamoto

Institutions: Universidad de Sevilla, The University of Tokyo

Language: English

Topic: Numerical methods in inverse problems

Subfield: Mathematical Physics

Field: Mathematics

Domain: Physical Sciences

Open Access status: hybrid

Estimated APC paid: $3,325