中山大学学报自然科学版 ›› 2019, Vol. 58 ›› Issue (3): 94-102.doi: 10.13471/j.cnki.acta.snus.2019.03.012

• 论文 • 上一篇    下一篇

癌症疫苗和抑制剂治疗模型整体解的存在唯一性

刘春燕1,卫雪梅1,冯兆永2,刘成霞3   

  1. 1. 广东工业大学应用数学学院,广东 广州 510520;
    2. 中山大学数学学院,广东 广州 510275;
    3. 南方医科大学口腔医院,广东 广州 510280
  • 收稿日期:2018-10-11 出版日期:2019-05-25 发布日期:2019-05-25
  • 通讯作者: 卫雪梅(1972年生),女;研究方向:偏微分方程;E-mail: wxm_gdut@163.com 刘成霞(1981年生),女;研究方向:口腔临床医学;E-mail: 349471214@qq.com

Existence and uniqueness of global solution for the treatment model of cancer vaccine and checkpoint inhibitor

LIU Chunyan1, WEI Xuemei1, FENG Zhaoyong2, LIU Chengxia3   

  1. 1. School of Applied Mathematics, Guangdong University of Technology, Guangzhou 510520, China;
    2. School of Mathematics, Sun Yat-sen University, Guangzhou 510275, China;
    3. Stomatological Hospital, Southern Medical University, Guangzhou 510280, China
  • Received:2018-10-11 Online:2019-05-25 Published:2019-05-25

摘要:

研究癌症疫苗和检查点抑制剂联合治疗的数学模型,该模型为包含九个相互耦合反应扩散方程的方程组。先通过运用Banach不动点定理、抛物型方程的 Lp 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。

关键词: 癌症疫苗, 检查点抑制剂, 联合治疗, 局部解, 整体解, 存在唯一性

Abstract:

A combined treatment model of cancer vaccine and checkpoint inhibitor, which contains nine coupled reaction diffusion equations, is studied. By using the Banach fixed point theorem and  Lp theory of parabolic equation, the existence and uniqueness of the model in the local solution is proved. And then the existence and uniqueness of the global solution is obtained by using the extension method.

Key words: cancer vaccine, checkpoint inhibitor, combined treatment, local solution, global solution, existence and uniqueness

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