Uniqueness in determining multidimensional domains with unknown initial data
Abstract
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.
Fields of Study & Subjects
Advanced Data Processing Techniques
Publication details
- Journal / source
- Inverse Problems
- Publisher
- IOP Publishing
- Volume
- 42
- Issue
- 9
- Pages
- 095005–095005
- Publication date
- 25 August 2026
- Language
- EN