| Global Existence for a Parabolic-hyperbolic Free Boundary Problem Modelling Tumor Growth |
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| 引用本文： | Shang-bin Cui Xue-mei Wei. Global Existence for a Parabolic-hyperbolic Free Boundary Problem Modelling Tumor Growth[J]. 应用数学学报(英文版), 2005, 21(4): 597-614. DOI: 10.1007/s10255-005-0268-1 |
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| 作者姓名： | Shang-bin Cui Xue-mei Wei |
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| 作者单位： | [1]Institute of Mathematics, Sun Yat-Sen University, Guangzhou 510275, China [2]Department of Mathematics, Sun Yat-Sen University, Guangzhou 510275 and Department of Applied Mathematics, Guangdong University of Technology, Guangzhou 510090, China |
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| 基金项目： | Supported by the National Natural Science Foundation of China （No.10171112）. |
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| 摘 要： |
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| 关 键 词： | 抛物线双曲线方程 自由边界问题 整体解 存在性 唯一性 |
| 收稿时间： | 2004-05-07 |
| 修稿时间： | 2004-05-072005-06-22 |
Global Existence for a Parabolic-hyperbolic Free Boundary Problem Modelling Tumor Growth |
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| Shang-bin Cui,Xue-mei Wei. Global Existence for a Parabolic-hyperbolic Free Boundary Problem Modelling Tumor Growth[J]. Acta Mathematicae Applicatae Sinica, 2005, 21(4): 597-614. DOI: 10.1007/s10255-005-0268-1 |
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| Authors: | Shang-bin Cui Xue-mei Wei |
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| Affiliation: | (1) Institute of Mathematics, Sun Yat-Sen University, Guangzhou 510275, China;(2) Department of Mathematics, Sun Yat-Sen University, Guangzhou 510275, China;(3) Department of Applied Mathematics, Guangdong University of Technology, Guangzhou 510090, China |
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| Abstract: | In this paper we study a free boundary problem modelling tumor growth, proposed by A. Friedman in 2004. This free boundary problem involves a nonlinear second-order parabolic equation describing the diffusion of nutrient in the tumor, and three nonlinear first-order hyperbolic equations describing the evolution of proliferative cells, quiescent cells and dead cells, respectively. By applying Lp theory of parabolic equations, the characteristic theory of hyperbolic equations, and the Banach fixed point theorem, we prove that this problem has a unique global classical solution. |
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| Keywords: | Free boundary problem tumor growth global solution existence uniqueness |
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