Article ID | Journal | Published Year | Pages | File Type |
---|---|---|---|---|
7222032 | Nonlinear Analysis: Real World Applications | 2018 | 16 Pages |
Abstract
We study a free boundary problem modeling solid tumor growth. The simplified model contains a parameter λ. Different from previous works on bifurcation analysis, a new ingredient of the present paper is that the influence of the extracellular matrix (ECM) and matrix degrading enzymes (MDE) interactions is included in the model. We first show that for each λ>0, there exists a unique radially symmetric stationary solution with radius r=RS. Then we prove that there exist a positive integer nâ and a sequence of λn(n>nâ) for which branches of symmetry-breaking stationary solutions bifurcate from the radially symmetric one. In particular, we discover that these λn are larger than those λËn previously known when the effects of ECM and MDE are not considered in the model.
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Authors
Hongjing Pan, Ruixiang Xing,