Carleman estimates for a magnetohydrodynamics system and application to inverse source problems (original) (raw)
Related papers
Inverse coefficients problem for a magnetohydrodynamics system
arXiv: Analysis of PDEs, 2018
In this article, we consider a magnetohydrodynamics system for incompressible flow in a three-dimensional bounded domain. Firstly, we give the stability results for our inverse coefficients problem. Secondly, we establish and prove two Carleman estimates for both direct problem and inverse problem. Finally, we complete the proof of stability result in terms of the above Carleman estimates.
Applicable Analysis, 2019
In this paper, we consider an inverse problem for the simultaneous diffusion process of elastic and electromagnetic waves in an isotropic heterogeneous elastic body which is identified with an open bounded domain. From the mathematical point of view, the system under consideration can be viewed as the coupling between the hyperbolic system of elastic waves and a parabolic system for the magnetic field. We study an inverse problem of determining the external source terms by observations data in a neighborhood of the boundary and we prove the Hölder stability. For the proof, we show a Carleman estimate for the displacement and the magnetic field of the magnetoelastic system.
Subdifferential Inverse Problems for Magnetohydrodynamics
Methods and Applications of Analysis, 2010
The theory of solvability of an abstract evolution inequality in a Hilbert space for the operators with the quadratic nonlinearity is presented. It is then applied for the study of an inverse problem for MHD flows. For the three-dimensional flows the global in time existence of the weak solutions to the inverse problem is proved. For the two-dimensional flows existence and uniqueness of the strong solutions are proved.
Stability for inverse source problems by Carleman estimates
2019
In this article, we provide a modified argument for proving conditional stability for inverse problems of determining spatially varying functions in evolution equations by Carleman estimates. Our method needs not any cut-off procedures and can simplify the existing proofs. We establish the conditional stability for inverse source problems for a hyperbolic equation and a parabolic equation, and our method is widely applicable to various evolution equations.
On the Inviscid and Non-Resistive Limit for the Equations of Incompressible Magnetohydrodynamics
Mathematical Models and Methods in Applied Sciences, 2002
We prove the convergence of the solutions for the incompressible homogeneous magnetohydrodynamics (MHD) system to the solutions to ideal MHD one in the inviscid and non-resistive limit, detailing the explicit convergence rates. For this study we consider a fluid occupying the whole space ℝ3 and we assume that the viscosity effects in this fluid can be described by two different operators: the usual Laplacian operator affected by the inverse of the Reynolds number or by a viscosity operator introduced by S. I. Braginskii in 1965.