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Determination of source and initial values for acoustic equations with a time-fractional attenuation
Xinchi Huang, Yavar Kian, Eric Soccorsi +1
We consider the inverse problem of determining the initial states or the source term of a hyperbolic equation damped by some non-local time-fractional derivative. This framework is…
Well-posedness and asymptotic estimate for a diffusion equation with time-fractional derivative
Zhiyuan Li, Xinchi Huang, Masahiro Yamamoto
In this paper, we study the asymptotic estimate of solution for a mixed-order time-fractional diffusion equation in a bounded domain subject to the homogeneous Dirichlet boundary c…
Inverse problems for a half-order time-fractional diffusion equation in arbitrary dimension by Carleman estimates
X. Huang, A. Kawamoto
We consider a half-order time-fractional diffusion equation in an arbitrary dimension and investigate inverse problems of determining the source term or the diffusion coefficient f…
Stability for inverse source problems by Carleman estimates
X. Huang, O. Yu. Imanuvilov, M. Yamamoto
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…
Inverse coefficients problem for a magnetohydrodynamics system
Xinchi Huang
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 coe…
Carleman estimate for the Schrödinger equation and application to magnetic inverse problems
Xinchi Huang, Yavar Kian, Eric Soccorsi +1
We prove that the stationary magnetic potential vector and the electrostatic potential entering the dynamic magnetic Schrödinger equation can be Lipschitz stably retrieved through…