# Inverse boundary problems: toward a unified theory

Main funder

Funder's project number: 309963

Funds granted by main funder (€)

- 564 000,00

Funding program

Project timetable

Project start date: 01/09/2017

Project end date: 31/08/2021

Summary

This proposal is concerned with the mathematical theory of inverse problems. This is a vibrant research field in the intersection of pure and applied mathematics, drawing techniques from several different areas and generating new research questions. Prominent questions include the Calder'on problem related to electrical imaging, the Gel'fand problem related to seismic imaging, and geometric inverse problems such as inversion of the geodesic X-ray transform. Recently, exciting new connections between these different topics have begun to emerge. This project intends to explore the possibility of a unified point of view to several inverse boundary problems and related consequences.

Principal Investigator

Primary responsible unit

Related publications and other outputs

- An inverse problem for a semi-linear wave equation : A numerical study (2024) Lassas, Matti; et al.; A1; OA
- Fixed Angle Inverse Scattering for Sound Speeds Close to Constant (2023) Ma, Shiqi; et al.; A1; OA
- On mixed and transverse ray transforms on orientable surfaces (2023) Ilmavirta, Joonas; et al.; A1; OA
- The Geodesic Ray Transform on Spherically Symmetric Reversible Finsler Manifolds (2023) Ilmavirta, Joonas; et al.; A1; OA
- An Inverse Problem for the Relativistic Boltzmann Equation (2022) Balehowsky, Tracey; et al.; A1; OA
- Fixed angle inverse scattering in the presence of a Riemannian metric (2022) Ma, Shiqi; et al.; A1; OA
- Inverse problems for elliptic equations with fractional power type nonlinearities (2022) Liimatainen, Tony; et al.; A1; OA
- Partial Data Problems and Unique Continuation in Scalar and Vector Field Tomography (2022) Ilmavirta, Joonas; et al.; A1; OA
- A sharp stability estimate for tensor tomography in non-positive curvature (2021) Paternain, Gabriel P.; et al.; A1; OA
- Free boundary methods and non-scattering phenomena (2021) Salo, Mikko; et al.; A1; OA