Bifurcation for a free-boundary tumor model with angiogenesis. (June 2017)

• Record Type: Journal Article
• Authors: Huang, Yaodan; Zhang, Zhengce; Hu, Bei
• Is Part Of: Nonlinear analysis. Volume 35(2017)
• Page Start: 483
• Page End: 502
• Publication Date: 2017-06
• Subjects: Bifurcation -- Free boundary problem -- Stationary solution -- Symmetry-breaking -- Angiogenesis; Nonlinear functional analysis -- Periodicals; Analyse fonctionnelle non linéaire -- Périodiques; Nonlinear functional analysis; Periodicals; 515.7248
• DOI: 10.1016/j.nonrwa.2016.12.003
• Languages: English
• ISSNs: 1468-1218

Abstract

Abstract: We consider a free boundary tumor model with vasculature which supply nutrients to the tumor, so that ∂ σ ∂ n + β ( σ − σ ¯ ) = 0 holds on the boundary, where a positive constant β is the rate of nutrient supply to the tumor and σ ¯ is the nutrient concentration outside the tumor. The tumor cells proliferate at a rate μ . We show that for each μ 2, μ 4, μ 6, μ 8, ⋯, symmetry-breaking stationary solutions bifurcate from the radially symmetric stationary solutions.