Uniqueness for an inverse problem for a nonlinear parabolic system with an integral term by one-point Dirichlet data
Laser-induced thermotherapy (LITT) is a cancer treatment that requires minimal invasion. The mathematical model of the LITT includes the so-called bio-heat equation for the unknown temperature $u$ in the tumor tissue and the Arrhenius-type equation for the distribution of native tissues. The key term of the model is the temperature-dependent function $f(u)$ that describes the coagulation growth kinetics. \par One can measure the temperature at the only point at the tumor tissue's boundary, and the inverse problem arises from the determination of $f$ based on this one-point measurement. Before beginning to solve the problem it is important to know if its solution is unique. To prove this fact, the authors first formulate and prove a comparison principle for temperatures $u$ in the LITT model that corresponds to different functions $f$. The uniqueness of the classical solution for the direct problem (with known $f$) is also discussed.
scientific article; zbMATH DE number 7040866