| Analysis of a Free Boundary Problem Modeling Tumor Growth |
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| 引用本文： | Shang Bin CUI （Shangbin CUI）. Analysis of a Free Boundary Problem Modeling Tumor Growth[J]. 数学学报(英文版), 2005, 21(5): 1071-1082. DOI: 10.1007/s10114-004-0483-3 |
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| 作者姓名： | Shang Bin CUI （Shangbin CUI） |
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| 作者单位： | Institute of Mathematics, Sun Yat-Sen University, Guangzhou 510275, P. R. China |
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| 基金项目： | Project supported by the China National Natural science Foundation, Grant number： 10171112 |
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| 摘 要： | In this paper, we study a free boundary problem arising from the modeling of tumor growth. The problem comprises two unknown functions： R = R（t）, the radius of the tumor, and u = u（r, t）, the concentration of nutrient in the tumor. The function u satisfies a nonlinear reaction diffusion equation in the region 0 〈 r 〈 R（t）, t 〉 0, and the function R satisfies a nonlinear integrodifferential equation containing u. Under some general conditions, we establish global existence of transient solutions, unique existence of a stationary solution, and convergence of transient solutions toward the stationary solution as t →∞.
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| 关 键 词： | 自由边界问题 广义解 渐进线 瘤生长模型 非线性扩散方程 |
| 收稿时间： | 2002-11-27 |
| 修稿时间： | 2002-11-272004-09-14 |
Analysis of a Free Boundary Problem Modeling Tumor Growth |
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| Shang Bin Cui. Analysis of a Free Boundary Problem Modeling Tumor Growth[J]. Acta Mathematica Sinica(English Series), 2005, 21(5): 1071-1082. DOI: 10.1007/s10114-004-0483-3 |
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| Authors: | Shang Bin Cui |
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| Affiliation: | Shangbin;CUI |
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| Abstract: | In this paper, we study a free boundary problem arising from the modeling of tumor growth. The problem comprises two unknown functions: R = R(t), the radius of the tumor, and u = u(r, t), the concentration of nutrient in the tumor. The function u satisfies a nonlinear reaction diffusion equation in the region 0 < r < R(t), t > 0, and the function R satisfies a nonlinear integrodi fferential equation containing u. Under some general conditions, we establish global existence of transient solutions, unique existence of a stationary solution, and convergence of transient solutions toward the stationary solution as t → ∞. Project supported by the China National Natural Science Foundation, Grant number: 10171112 |
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| Keywords: | Free boundary problem Tumor growth Global solution Asymptotic behavior |
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