We consider optimal control of the scalar wave equation where the control enters as a coefficient in the principal part. Adding a total variation penalty allows showing existence of optimal controls, which requires continuity results for the coefficient-to-solution mapping for discontinuous coefficients. We additionally consider a so-called multi-bang penalty that promotes controls taking on...
A very common ansatz in inverse problems for PDEs is that the sought solutions are piecewise constant, modelling situations like localized inclusions of different material properties within an otherwise homogeneous medium. In this situation, variational regularization with a total variation penalty balances being compatible with piecewise constant minimizers with retaining convexity of the...
Detecting ischemic regions is paramount in preventing potentially fatal ventricular ischemic tachycardia. Traditionally, this involves capturing the heart's electrical activity through noninvasive or minimally invasive methods, such as body surface or intracardiac measurements. Insight into utilizing electrical measurements for ischemia detection can be gained through mathematical and...
Several applications in medical imaging and non-destructive material testing lead to inverse elliptic coefficient problems, where an unknown coefficient function in an elliptic PDE is to be determined from partial knowledge of its solutions. This is usually a highly non-linear ill-posed inverse problem, for which unique reconstructability results, stability and resolution estimates and global...
Domain derivatives have been studied for a variety of time-harmonic scattering problems featuring different partial differential equations, boundary conditions and geometrical configurations.
The aim of this presentation is to establish the temporal domain derivative for the acoustic wave equation when a sound-soft scattering object is present.
In our analysis we proceed through the Laplace...
The forward and adjoint problems in photoacoustic tomography can be modelled as an initial value and a time varying source problem for the free space wave equation. Despite the advances made in recent years (parallel interrogation with up to 64 beams), the data acquisition time in state-of-the-art PAT scanners is still a bottle-neck resulting in sparse, limited angle data. The solution of...
Many processes in cells are driven by the interaction of multiple proteins, for example cell contraction, division or migration. Two important types of proteins are actin filaments and myosin motors. Myosin is able to bind to and move along actin filaments with its two ends, leading to the formation of a dynamic actomyosin network, in which stresses are generated and patterns may form....
We investigate the ill-posed inverse problem of recovering unknown spatially dependent parameters in nonlinear evolution PDEs. We propose a bi-level Landweber scheme, where the upper-level parameter reconstruction embeds a lower-level state approximation. This can be seen as combining the classical reduced setting and the newer all-at-once setting, allowing us to, respectively, utilize...
This work presents an inverse problem where we seek to recover the discontinuity jump of the displacements field that verifies a linear elasticity equation, from measurements of the displacement field or traction field on a subdomain of the bordary. This inverse problem allows us to study subduction earthquakes, which are of great importance to the geophysical community.
To obtain the...
