264 citations · 659 across the 23 of their papers we have counts for
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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…
Determining the nonlinearity in an acoustic wave equation
Barbara Kaltenbacher, William Rundell
We consider an undetermined coefficient inverse problem for a nonlinear partial differential equation describing high intensity ultrasound propagation as widely used in medical ima…
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…