Carleman estimates for a magnetohydrodynamics system and application to inverse source problems
Xinchi Huang, Masahiro Yamamoto
TL;DR
This paper establishes Carleman estimates for a linearized magnetohydrodynamics system and uses them to derive stability results for inverse source problems in a 3D domain.
Contribution
It introduces new Carleman estimates tailored for MHD systems and applies them to inverse source problems, advancing stability analysis in this context.
Findings
Proved two types of Carleman estimates for the MHD system
Established Holder stability for inverse source problems
Combined parabolic and elliptic Carleman estimates effectively
Abstract
In this article, we consider a linearized magnetohydrodynamics system for incompressible flow in a three-dimensional bounded domain. We first prove two kinds of Carleman estimates. This is done by combining the Carleman estimates for the parabolic and the elliptic equations. Then we apply the Carleman estimates to prove Holder type stability results for some inverse source problems.
Peer Reviews
No public reviews on file for this paper yet. If you reviewed it on a platform where reviews are public (OpenReview, ICLR, NeurIPS, ICML), you can paste yours below so the community can read it here.
Videos
No videos yet. Explain this paper in a talk, walkthrough, or lecture? Add one.
Taxonomy
TopicsNumerical methods in inverse problems · Advanced Mathematical Physics Problems · Stability and Controllability of Differential Equations