220 citations · 1.5k across the 94 of their papers we have counts for
10 papers · 2 filters
Identification of time-varying source term in time-fractional diffusion equations
Yavar Kian, Eric Soccorsi, Qi Xue +1
This paper is concerned with the inverse problem of determining the time and space dependent source term of diffusion equations with constant-order time-fractional derivative in $(…
Uniqueness of solution of an inverse source problem for ultrahyperbolic equations
Fikret Gölgeleyen, Masahiro Yamamoto
The aim of this article is to investigate the uniqueness of solution of an inverse problem for ultrahyperbolic equations. We first reduce the inverse problem to a Cauchy problem fo…
Unique determination of several coefficients in a fractional diffusion(-wave) equation by a single measurement
Yavar Kian, Zhiyuan Li, Yikan Liu +1
We consider the inverse problem of determining different type of information about a diffusion process, described by ordinary or fractional diffusion equations stated on a bounded…
Inverse moving source problem for fractional diffusion(-wave) equations: Determination of orbits
Guanghui Hu, Yikan Liu, Masahiro Yamamoto
This paper is concerned with the inverse problem on determining an orbit of the moving source in a fractional diffusion(-wave) equations in a connected bounded domain of $\mathbb R…
Inverse Problems of Determining Coefficients of the Fractional Partial Differential Equations
Zhiyuan Li, Masahiro Yamamoto
When considering fractional diffusion equation as model equation in analyzing anomalous diffusion processes, some important parameters in the model, for example, the orders of the…
Inverse Problems of Determining Parameters of the Fractional Partial Differential Equations
Zhiyuan Li, Yikan Liu, Masahiro Yamamoto
When considering fractional diffusion equation as model equation in analyzing anomalous diffusion processes, some important parameters in the model related to orders of the fractio…
Inverse Problems of Determining Sources of the Fractional Partial Differential Equations
Yikan Liu, Zhiyuan Li, Masahiro Yamamoto
In this chapter, we mainly review theoretical results on inverse source problems for diffusion equations with the Caputo time-fractional derivatives of order . Our surve…
Unique continuation property with partial information for two-dimensional anisotropic elasticity systems
Jin Cheng, Yikan Liu, Yanbo Wang +1
In this paper, we establish a novel unique continuation property for two-dimensional anisotropic elasticity systems with partial information. More precisely, given a homogeneous el…
Inverse coefficient problems for a transport equation by local Carleman estimate
Piermarco Cannarsa, Giuseppe Floridia, Fikret Gölgeleyen +1
We consider the transport equation $\ppp_tu(x,t) + (H(x)\cdot \nabla u(x,t)) + p(x)u(x,t) = 0$ in $\OOO \times (0,T)$ where $\OOO \subset \R^n$ is a bounded domain, and discuss two…
Reconstruction and stable recovery of source terms and coefficients appearing in diffusion equations
Yavar Kian, Masahiro Yamamoto
We consider the inverse source problem of determining a source term depending on both time and space variable for fractional and classical diffusion equations in a cylindrical doma…