| 报告题目： | Modelling and optimal control of solid-solid phase transitions - from surface hardening of steel to laser thermo-therapy |
| 报 告 人： | Prof. Dr. Dietmar Hoemberg |
| WIAS Inst. f. Mathematik, Germany | |
| 报告时间： | 3月28日（星期一）下午 2:00 |
| 报告地点： | 九龙湖数学系第一报告厅 |
| 相关介绍： | Astract： In the first part of my talk I will give a short review of classical phase transition models and derive a thermo-mechanical model based on rate laws for the phase fractions accounting in addition for mechanical effects. In the second part we apply the model to the surface hardening of steel. Since the penetration depth is small (often less then a millimeter) compared to the workpiece dimension, adaptivity in space and time is decisive for the numerical simulation of laser treatments. > In the last part of the talk we apply the phase transition model to the case of laser thermo-therapy. This is a minimal invasive cancer treatment in which necrotic tissue is coagulated and thus destroyed. Since the temporal monitoring of the therapy is difficult, simulations are very important to estimate the optimal dosage. To this end we investigate a corresponding inverse problem of identifying the thermal growth characteristics of the coagulated tissue. We reformulate the problem in terms of an optimal control problem, prove existence of a solution, derive optimality conditions, and conclude with some numerical results. http://www.math.TU-Berlin.de/~hoemberg |
