Existence and Uniqueness of Global Solution for a Model of Retinal Oxygen Distribution and the Role of Neuroglobin

Chen Mei-gui; Wei Xue-mei

doi:10.12052/gdutxb.170178

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Existence and Uniqueness of Global Solution for a Model of Retinal Oxygen Distribution and the Role of Neuroglobin

更新时间：2026-05-27

- Existence and Uniqueness of Global Solution for a Model of Retinal Oxygen Distribution and the Role of Neuroglobin
- Vol. 35, Issue 5, Pages: 45-50(2018)
- 作者机构：
  
  广东工业大学　应用数学学院,广东,广州,510520
- 作者简介：
- 基金信息：
- DOI：10.12052/gdutxb.170178
  CLC： O175
- Online First：10 July 2018，
  
  Published：2018
- 稿件说明：
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陈美癸, 卫雪梅. 视网膜氧分布与脑红蛋白作用模型解的存在唯一性[J]. 广东工业大学学报, 2018, 35(5): 45-50.

Chen Mei-gui, Wei Xue-mei. Existence and Uniqueness of Global Solution for a Model of Retinal Oxygen Distribution and the Role of Neuroglobin[J]. 2018, 35(5): 45-50.
陈美癸, 卫雪梅. 视网膜氧分布与脑红蛋白作用模型解的存在唯一性[J]. 广东工业大学学报, 2018, 35(5): 45-50. DOI： 10.12052/gdutxb.170178.

Chen Mei-gui, Wei Xue-mei. Existence and Uniqueness of Global Solution for a Model of Retinal Oxygen Distribution and the Role of Neuroglobin[J]. 2018, 35(5): 45-50. DOI： 10.12052/gdutxb.170178.

摘要

研究视网膜中氧分布与脑红蛋白作用的数学模型

该模型包含了4组相互耦合的反应扩散方程组. 先通过运用Banach不动点定理

抛物型方程的

估计证明了模型的局部解的存在唯一性

然后利用延拓方法得到了整体解的存在唯一性.

Abstract

A study is conducted on a mathematical model of retina oxygen distribution and the role of neuroglobin

which contains four sets of mutually coupled reaction diffusion equations. The existence and uniqueness of the model in the local solution is proved by using the Banach Fixed Point Theorem

applying

-theory of parabolic equation. And then the existence and uniqueness of the global solution is obtained by using the extension method.

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Keywords

references

ANDERSON B, SALTZMAN H A. Retinal oxygen utilization measured by hyperbaric blackout [J]. Arch Ophthalmol, 1964, 72(6): 792-795.

ANDERSON B. Ocular effects of changes in oxygen and carbon dioxide tension [J]. Trans Am Ophthalmol Soc, 1968, 66: 423-474.

YU D Y, CRINGLE S J. Oxygen distribution and consumption within the retina in vascularised and avascular retinas and in animal models of retinal disease [J]. Prog Retin Eye Res, 2001, 20(2): 175-208.

WANGSA-WIRAWAN N D, LINSENMEIER R A. Retinal oxygen: fundamental and clinical aspects [J]. Arch Ophthalmol, 2003, 121(4): 547-557.

YU D Y, CRINGLE S J, VALTER K, et al . Photoreceptor death, trophic factor expression, retinal oxygen status, and photoreceptor function in the P23H rat [J ] . Invest Ophthalmol Vis Sci, 2004, 45(6): 2013-2019.

STEFANSSON E. Retinal oxygen tension is higher in light than dark [J]. Pediatr Res, 1988, 23(1): 5-8.

PADNICK-SILVER L, LINSENMEIER R A. Effect of acute hyperglycemia on oxygen and oxidative metabolism in the intact cat retina [J]. Invest Ophthalmol Vis Sci, 2003, 44(2): 745-750.

YU D Y, CRINGLE S J, SU E N. Intraretinal oxygen distribution in the monkey retina and the response to systemic hyperoxia [J]. Invest Ophthalmol Vis Sci, 2005, 46(12): 4728-4733.

KOHEN R, NYSKA A. Invited review: oxidation of biological systems: oxidative stress phenomena, antioxidants, redox reactions, and methods for their quantification [J]. Toxicol Pathol, 2002, 30(6): 620-650.

CRINGLE S J, YU D Y. A multi-layer model of retinal oxygen supply and consumption helps explain the muted rise in inner retinal PO(2) during systemic hyperoxia [J]. Comparative Biochemistry Physiology Part A, 2002, 132(1): 61-66.

YU D Y, CRINGLE S J. Outer retinal anoxia during dark adaptation is not a general property of mammalian retinas [J]. Comparative Biochemistry Physiology Part A, 2002, 132(1): 47-52.

ROBERTS P A, GAFFNEY E A, LUTHERT P J, et al . Retinal oxygen distribution and the role of neuroglobin [J ] . Journal of Mathematical Biology, 2016, 73(1): 1-38.

姜礼尚, 陈亚浙. 数学物理方程讲义[M]. 北京: 高等教育出版社, 2007.

FRIEDMAN A, LOLAS G. Analysis of a mathematical model of tumor lymphangiogenesis [J]. Math Models Methods Appl Sci, 2005, 15: 95-107.

CUI S B, WEI X M. Global existence for a parabolic-hyperbolic free boundary problem modelling tumor growth [J]. Acta Math Appl Sinica, English series, 2005, 4: 597-614.

WEI X M, GUO C. Global Existence for a mathematical model of the immune response to canner [J]. Nonlinear Analysis: Real World Applications, 2010(11): 3903-3911.

WEI X M, CUI S B. Existence and uniqueness of the global solution for a mathematical model of the use of macrophages in tumor medicine [J]. Nonlinear Analysis: Real World Applications, 2007, 8: 922-938.

WEI X M, CUI S B. Existence and uniqueness of global solutions for a mathematical model of antiangiogenesis in tumor growth [J]. Nonlinear Analysis: Real World Applications, 2008, 9(5): 1827-1836.

WEI X M. Global existence for a free boundary problem modeling the growth of necrotic tumors in the presence of inhibitors [J]. Inter Pure Appl. Math, 2006, 280: 321-338.

崔尚斌. 偏微分方程现代理论引论[M]. 北京: 科学出版社, 2015.

LADYZENSKAJA O A, SOLONNIKOV V A, URALCEVA N N. Linear and quasilinear partial differential equations of parabolic type, translations of mathematical monographs [M]. Amer Math Soc, 1968, 23.

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