Continuation Along Bifurcation Branches for a Tumor Model with a Necrotic Core |
| |
Authors: | Wenrui Hao Jonathan D Hauenstein Bei Hu Yuan Liu Andrew J Sommese Yong-Tao Zhang |
| |
Affiliation: | 1. Department of Applied and Computational Mathematics and Statistics, University of Notre Dame, Notre Dame, IN, 46556, USA 2. Department of Mathematics, Texas A&M University, College Station, TX, 77843-3368, USA
|
| |
Abstract: | We consider a free boundary problem for a system of partial differential equations, which arises in a model of tumor growth with a necrotic core. For any positive number R and 0<??<R, there exists a radially-symmetric stationary solution with tumor free boundary r=R and necrotic free boundary r=??. The system depends on a positive parameter ??, which describes tumor aggressiveness, and for a sequence of values ?? 2<?? 3<??, there exist branches of symmetry-breaking stationary solutions, which bifurcate from these values. Upon discretizing this model, we obtain a family of polynomial systems parameterized by tumor aggressiveness factor???. By continuously changing ?? using a homotopy, we are able to compute nonradial symmetric solutions. We additionally discuss linear and nonlinear stability of such solutions. |
| |
Keywords: | |
本文献已被 SpringerLink 等数据库收录! |
|