22 citations · 29 across the 9 of their papers we have counts for
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Identification of space-dependent coefficients in two competing terms of a nonlinear subdiffusion equation
Barbara Kaltenbacher, William Rundell
We consider a (sub)diffusion equation with a nonlinearity of the form , where and are space dependent functions. Prominent examples are the Fisher-KPP, the Frank-…
Reconstruction of space-dependence and nonlinearity of a reaction term in a subdiffusion equation
Barbara Kaltenbacher, William Rundell
In this paper we study the simultaneous reconstruction of two coefficients in a reaction-subdiffusion equation, namely a nonlinearity and a space dependent factor. The fact that th…
Regularising the Cauchy problem for Laplace's equation by fractional operators
Barbara Kaltenbacher an William Rundell
In this paper we revisit the classical Cauchy problem for Laplace's equation as well as two further related problems in the light of regularisation of this highly ill-conditioned p…
Nonlinearity parameter imaging in the frequency domain
Barbara Kaltenbacher, William Rundell
Nonlinearity parameter tomography leads to the problem of identifying a coefficient in a nonlinear wave equation (such as the Westervelt equation) modeling ultrasound propagation.…
The Inverse Problem of Reconstructing Reaction-Diffusion Systems
Barbara Kaltenbacher, William Rundell
This paper considers the inverse problem of recovering state-dependent source terms in a reaction-diffusion system from overposed data consisting of the values of the state variabl…
Regularization of a backwards parabolic equation by fractional operators
Barbara Kaltenbacher, William Rundell
The backwards diffusion equation is one of the classical ill-posed inverse problems, related to a wide range of applications, and has been extensively studied over the last 50 year…