Uniqueness and stability of inverse space-dependent source problems in hyperbolic bio-heat transfer

This paper considers the linear but ill-posed inverse problems concerned with the determination of both the temperature and the source in the thermal-wave hyperbolic model of heat transfer in biological tissues. The heterogeneous source includes an unknown space-dependent component that has to be retrieved from extra temperature measurements at the final time or from time-average temperature integral observations. In contrast to the previous research on the parabolic bio-heat transfer equation, the present study takes into account for the realistic final speed of heat propagation in biological tissues. The approach to prove the uniqueness and stability is based on integral identities.