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数学学院、所系列学术报告(734场):北京大学周珍楠教授

发表于: 2017-09-20 09:10  点击:

  目 :An accurate front capturing scheme for tumor growth models with a free boundary limit 

 

报告人:北京大学  周珍楠教授

 

  间:2017年9月21日上午10:00-11:00

 

  点:数学楼一楼报告厅

 

  要:In this talk, I will present some recent work on the tumor growth equation along with various models for the nutrient component, including the in vitro model and the in vivo model. At the cell density level, the spatial availability of the tumor density $n$ is governed by the Darcy law via the pressure $p(n) = n^m$. As $m$ goes to infinity, the cell density models formally converge to Hele-Shaw flow models, which determine the free boundary dynamics of the tumor tissue in the incompressible limit. We derive several analytical solutions to the Hele-Shaw flow models, which serve as benchmark solutions to the geometric motion of tumor front propagation. Also, we develop a numerical scheme based on a novel prediction-correction reformulation that can accurately approximate the front propagation even when the nonlinearity is extremely strong. We show that the semi-discrete scheme naturally connects to the free boundary limit equation as $m$ goes to infinity, and with proper spatial discretization, the fully discrete scheme has improved stability, preserves positivity, and implements without nonlinear solvers. This is a joint work with Jian-Guo Liu, Min Tang and Li Wang.