Nataliia Kinash (University of Leeds) – Recovering a space-dependent heat source in the Maxwell–Cattaneo bio-heat model

Thermal therapies such as hyperthermia, laser ablation, and high-intensity focused ultrasound rely on delivering controlled heat to biological tissue. The temperature propagation in the tissue cannot be modelled accurately with the  Fourier's law, but should be modelled with the Maxwell–Cattaneo law instead, which gives rise to the hyperbolic bio-heat equation, that incorporates the assumption of the finite speed propagation. In this talk I will discuss inverse source problems for such a hyperbolic model, where the goal is to recover the unknown space-dependent component of the heat source.