Bifurcation for a free boundary problem modeling the growth of a tumor with a necrotic core |
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Authors: | Wenrui Hao Jonathan D Hauenstein Bei Hu Yuan Liu Yong-Tao Zhang |
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Institution: | a Department of Applied and Computational Mathematics and Statistics, University of Notre Dame, Notre Dame, IN 46556, USAb Department of Mathematics, Mailstop 3368, Texas A&M University, College Station, TX 77843, USA |
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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 numbers ρ<R, there exists a radially symmetric stationary solution with tumor boundary r=R and necrotic core boundary r=ρ. The system depends on a positive parameter μ, which describes the tumor aggressiveness. There also exists a sequence of values μ2<μ3<? for which branches of symmetry-breaking stationary solutions bifurcate from the radially symmetric solution branch. |
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Keywords: | Bifurcation Free boundary problem Tumor model Necrotic core |
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