TY - GEN A1 - Hömberg, Dietmar A1 - Liu, Jijun A1 - Togobytska, Nataliya T1 - Identification of the thermal growth characteristics of coagulated tumor tissue in laser-induced thermotherapy N2 - We consider an inverse problem arising in laser-induced thermotherapy, a minimally invasive method for cancer treatment, in which cancer tissue is destroyed by coagulation. For the dosage planning numerical simulation plays an important role. To this end a crucial problem is to identify the thermal growth kinetics of the coagulated zone. Mathematically, this problem is a nonlinear and nonlocal parabolic heat source inverse problem. The solution to this inverse problem is defined as the minimizer of a non-convex cost functional. The existence of the minimizer is proven. We derive the Gateaux derivative of the cost functional, which is based on the adjoint system, and use it for a numerical approximation of the optimal coefficient. KW - inverse problem KW - nonlinear equation KW - optimal control KW - iteration scheme KW - coupled system KW - numerics Y1 - 2011 UR - https://opus4.kobv.de/opus4-matheon/frontdoor/index/index/docId/804 UR - https://nbn-resolving.org/urn:nbn:de:0296-matheon-8041 ER -