Paper Info
Title
Bifurcation of a Mathematical Model for Tumor Growth with Angiogenesis and Gibbs-Thomson Relation
Abstract
In this paper, a mathematical model for solid vascular tumor growth with Gibbs-Thomson relation is studied. On the free boundary, we consider Gibbs-Thomson relation which means energy is expended to maintain the tumor structure. Supposing that the nutrient is the source of the energy, the nutrient denoted by sigma satisfies partial derivative(n)sigma + alpha[sigma - (sigma) over bar (1 - gamma k)] = 0 on partial derivative Omega, where alpha > 0 is a constant representing the ability of the tumor to absorb the nutrient through its blood vessels; (sigma) over bar is concentration of the nutrient outside the tumor; k is the mean curvature; gamma denotes adhesiveness between cells and partial derivative(n)sigma denotes the exterior normal derivative on partial derivative Omega. The existence, uniqueness and nonexistence of radially symmetric solutions are discussed. By using the bifurcation method, we discuss the existence of nonradially symmetric solutions. The results show that infinitely many nonradially symmetric solutions bifurcate from the radially symmetric solutions.
Year
DOI
Venue
2021
10.1142/S0218127421502321
INTERNATIONAL JOURNAL OF BIFURCATION AND CHAOS
Keywords
DocType
Volume
Solid vascular tumor, free boundary problem, stationary solution, bifurcation
Journal
31
Issue
ISSN
Citations 
15
0218-1274
0
PageRank 
References 
Authors
0.34
0
3
Name
Order
Citations
PageRank
Shihe Xu101.35
Meng Bai200.34
Fangwei Zhang3157.07