Carleman estimates for a magnetohydrodynamics system and application to inverse source problems

Xinchi Huang; Masahiro Yamamoto

doi:10.3934/mcrf.2022005

Article Contents

2023, Volume 13, Issue 2: 470-499. Doi: 10.3934/mcrf.2022005

This issue Previous Article A semigroup approach to stochastic systems with input delay at the boundary Next Article The discretized backstepping method: An application to a general system of

$ 2\times 2 $

linear balance laws

Carleman estimates for a magnetohydrodynamics system and application to inverse source problems

Xinchi Huang^1,2, , and
Masahiro Yamamoto^1,3,4,

1.
Graduate School of Mathematical Sciences, The University of Tokyo, 3-8-1 Komaba, Meguro, Tokyo, 153-8914, Japan
2.
JSPS Postdoctoral Fellowships for research in Japan
3.
Honorary Member of Academy of Romanian Scientists, Ilfov, nr. 3, Bucuresti, Romania
4.
Correspondence member of Accademia Peloritana dei Pericolanti, Palazzo Università, Piazza S. Pugliatti 1 98122 Messina, Italy

^*Corresponding author: Xinchi Huang
^*Corresponding author: Xinchi Huang

Received: July 2021

Revised: November 2021

Early access: March 2022

Published: June 2023

The first author is supported by JSPS grant 20F20319, the second author is supported by JSPS grant 20H00117, NSFC grant 11771270, 91730303

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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 Hölder type stability results for some inverse source problems.

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Mathematics Subject Classification: Primary: 35R30, 35Q35.

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References

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