Traveling wavefronts of a nonlinear reaction-diffusion model of tumor growth under the acid environment
被引量:2
Traveling wavefronts of a nonlinear reaction-diffusion model of tumor growth under the acid environment
摘要
In this paper, a reaction-diffusion model describing temporal development of tumor tissue, normal tissue and excess H+ ion concentration is considered. Based on a combi- nation of perturbation methods, the Fredholm theory and Banach fixed point theorem, we theoretically justify the existence of the traveling wave solution for this model.
参考文献12
-
1N. Bellomo and L. Preziosi, Modeling and mathematical problems related to tumor evolution and its interaction with the immune system, Math. Comput. Model. 32 (2000) 413-452.
-
2T. Faria, W. Huang and J. Wu, Travelling waves for delayed reaction-diffusion equations with global response, Proc. Roy. Soc. London Ser. A 462 (2006) 229-261.
-
3R. A. Gatenby, Models of tumor host interaction as competing populations: Implications for tumor biology and treatment, J. Theor. Bioi. 176 (1995) 447-455.
-
4R. A. Gatenby and E. T. Gawlinski, A reaction-diffusion model of cancer invasion, Cancer Res. 56 (1996) 5745-5753.
-
5S. Michelson and J. Leith, Autocrine and paracrine growth factors in tumor growth: A mathematical model, Bull. Math. BioI. 53 (1991) 639-656.
-
6K. Mischaikow, H. Smith and H. R. Thieme, Asymptotically autonomous semiflows: Chain recurrence and Lyapunov functions, Trans. Amer. Math. Soc. 347 (1995) 1669- 1685.
-
7J. D. Murray, Mathematical Biology, Vols. I and II (Springer-Verlag, New York, 2002).
-
8K. J. Palmer, Exponential dichotomies and transversal homo clinic points, J. Differential Equations 55 (1984) 225-256.
-
9J. A. Sherratt, Cellular growth control and traveling waves of cancer, SIAM J. Appl. Math. 53 (1993) 1713-1730.
-
10J. A. Sherratt, Wavefront propagation in a competition equation with a new motility term modeling contact inhibition between cell populations, Proc. Roy. Soc. London Ser. A 456 (2000) 2365-2386.
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-
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-
1王秀芳,朱惠延,王芳娟.酸性环境下肿瘤生长反应扩散方程模型的行波解[J].南华大学学报(自然科学版),2011,25(4):65-69.
-
2田静,陈勇.Effect of Time Delay on Stochastic Tumor Growth[J].Chinese Physics Letters,2010,27(3):48-51.
-
3MA Man-jun,LI Hui,GAO Mei-yan,TAO Ji-cheng,HAN Ya-zhou.Traveling wavefronts for a reaction-diffusion-chemotaxis model with volume-filling effect[J].Applied Mathematics(A Journal of Chinese Universities),2017,32(1):108-116.
-
4HUANG Ye-hui WENG Pei-xuan.Spreading Speed for a Periodic Reaction-diffusion Model with Nonmonotone Birth Function[J].Chinese Quarterly Journal of Mathematics,2012,27(3):467-474.
-
5吴俊林,黄新民.Density fluctuation of the ^3He reaction-diffusion model in nonextensive statistical mechanics[J].Chinese Physics B,2007,16(11):3216-3219.
-
6Shang Bin CUI (Shangbin CUI).Analysis of a Free Boundary Problem Modeling Tumor Growth[J].Acta Mathematica Sinica,English Series,2005,21(5):1071-1082. 被引量:10
-
7Jing ZHANG Yi CHEN Xian-liang XIN Qiu-ning LI Ming LI Li-ping LIN Mei-yu GENG Jian DING.Oligomannurarate sulfate blocks tumor growth by inhibiting NF-κB activation[J].Acta Pharmacologica Sinica,2010,31(3):375-381. 被引量:2
-
8张为付,吕荣庆.两种生物相互作用的反应扩散模型及解的讨论[J].应用数学,1995,8(3):371-374.
-
9Inhibitory Effects of Oxygen Ion Irradiation on Murine Tumor Growth[J].IMP & HIRFL Annual Report,1997(0):78-78.
-
10Weihua Jiang,Xin Li,XingfuZou.On a reaction-diffusion model for sterile insect release method on a bounded domain[J].International Journal of Biomathematics,2014,7(3):119-135.