38 citations · 50 across the 9 of their papers we have counts for
9 papers
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…
A preconditioner based on sine transform for two-dimensional Riesz space factional diffusion equations in convex domains
Xin Huang, Hai-Wei Sun
In this paper, we develop a fast numerical method for solving the time-dependent Riesz space fractional diffusion equations with a nonlinear source term in the convex domain. An im…
Spectral analysis for preconditioning of multi-dimensional Riesz fractional diffusion equations
Xin Huang, Xue-Lei Lin, Michael K. Ng +1
In this paper, we analyze the spectra of the preconditioned matrices arising from discretized multi-dimensional Riesz spatial fractional diffusion equations. The finite difference…
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…
Initial-boundary value problems for multi-term time-fractional diffusion equations with x-dependent coefficients
Zhiyuan Li, Xinchi Huang, Masahiro Yamamoto
In this paper, we discuss an initial-boundary value problem (IBVP) for the multi-term time-fractional diffusion equation with x-dependent coefficients. By means of the Mittag-Leffl…