264 citations · 659 across the 23 of their papers we have counts for
10 papers · 1 filter
Determining damping terms in fractional wave equations
Barbara Kaltenbacher, William Rundell
This paper deals with the inverse problem of recovering an arbitrary number of fractional damping terms in a wave equation. We develop several approaches on uniqueness and reconstr…
On an inverse problem of nonlinear imaging with fractional damping
Barbara Kaltenbacher, William Rundell
This paper considers the attenuated Westervelt equation in pressure formulation. The attenuation is by various models proposed in the literature and characterised by the inclusion…
On the identification of the nonlinearity parameter in the Westervelt equation from boundary measurements
Barbara Kaltenbacher, William Rundell
We consider an undetermined coefficient inverse problem for a non-\\linear partial differential equation occurring in high intensity ultrasound propagation as used in acoustic tomo…
On uniqueness and reconstruction of a nonlinear diffusion term in a parabolic equation
Barbara Kaltenbacher, William Rundell
The problem of recovering coefficients in a diffusion equation is one of the basic inverse problems. Perhaps the most important term is the one that couples the length and time sca…
On the simultaneous recovery of the conductivity and the nonlinear reaction term in a parabolic equation
Barbara Kaltenbacher, William Rundell
This paper considers the inverse problem of recovering both the unknown, spatially-dependent conductivity and the nonlinear reaction term in a reaction-diffusion equa…
Uniqueness for an inverse coefficient problem for a one-dimensional time-fractional diffusion equation with non-zero boundary conditions
W. Rundell, M. Yamamoto
We consider initial boundary value problems for one-dimensional diffusion equation with time-fractional derivative of order which are subject to non-zero Neumann bound…
On the identification of source term in the heat equation from sparse data
William Rundell, Zhidong Zhang
We consider the recovery of a source term for the nonhomogeneous heat equation in where is a bounded domain in with smooth…
A direct method for reconstructing inclusions and boundary conditions from electrostatic data
Isaac Harris
In this paper, we will discuss the use of a Sampling Method to reconstruct impenetrable inclusions from Electrostatic Cauchy data. We consider the case of a perfectly conducting an…
Fraction diffusion: Recovering the distributed fractional derivative from overposed data
William Rundell, Zhidong Zhang
There has been considerable recent study in "sub-diffusion" models that replace the standard parabolic equation model by a one with a fractional derivative in the time variable. Th…
Strong maximum principle for fractional diffusion equations and an application to an inverse source problem
Yikan Liu, William Rundell, Masahiro Yamamoto
The strong maximum principle is a remarkable characterization of parabolic equations, which is expected to be partly inherited by fractional diffusion equations. Based on the corre…