Existence analysis of solutions of a class of cross diffusion equations on the mechanism of drug resistance of melanoma

CHEN Wei; WEI Xuemei; FENG Zhaoyong; LIU Chengxia

doi:10.13471/j.cnki.acta.snus.2022A040

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Existence analysis of solutions of a class of cross diffusion equations on the mechanism of drug resistance of melanoma

Research articles | 更新时间：2023-11-01

- Existence analysis of solutions of a class of cross diffusion equations on the mechanism of drug resistance of melanoma
- Acta Scientiarum Naturalium Universitatis Sunyatseni Vol. 62, Issue 3, Pages: 137-148(2023)
- 作者机构：
  
  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
- 作者简介：
  
  CHEN Wei (2801978117@qq.com)
  WEI Xuemei (wxm_gdut@163.com
  FENG Zhaoyong （fzhaoy@mail.sysu.edu.cn）
  LIU Chengxia (349471214@qq.com)
- 基金信息：
- DOI：10.13471/j.cnki.acta.snus.2022A040
  CLC： O175
- Published：25 May 2023，
  
  Published Online：27 March 2023，
  
  Received：21 April 2022，
  
  Accepted：30 August 2022
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陈为,卫雪梅,冯兆永等.一类黑色素瘤耐药机制交叉扩散方程组模型解的存在性[J].中山大学学报(自然科学版),2023,62(03):137-148.

CHEN Wei,WEI Xuemei,FENG Zhaoyong,et al.Existence analysis of solutions of a class of cross diffusion equations on the mechanism of drug resistance of melanoma[J].Acta Scientiarum Naturalium Universitatis Sunyatseni,2023,62(03):137-148.
陈为,卫雪梅,冯兆永等.一类黑色素瘤耐药机制交叉扩散方程组模型解的存在性[J].中山大学学报(自然科学版),2023,62(03):137-148. DOI： 10.13471/j.cnki.acta.snus.2022A040.

CHEN Wei,WEI Xuemei,FENG Zhaoyong,et al.Existence analysis of solutions of a class of cross diffusion equations on the mechanism of drug resistance of melanoma[J].Acta Scientiarum Naturalium Universitatis Sunyatseni,2023,62(03):137-148. DOI： 10.13471/j.cnki.acta.snus.2022A040.

摘要

研究了检查点抑制剂靶向治疗人类黑色素瘤的数学模型。该模型由12个耦合的反应扩散方程组成，模型具有不连续项且包含自由边界条件。将自由边界问题转化为固定边界问题，并利用抛物方程的

https://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=49418995&type=

https://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=49418990&type=

2.62466669

2.53999996

理论和Schauder不动点定理，结合函数逼近的方法，得到了该数学模型全局弱解的存在性。

Abstract

A mathematical model of checkpoint inhibitor targeted therapy for human melanoma is investigated. The model consists of twelve coupled reaction-diffusion equations

which includes free boundary conditions and discontinuous terms. By transforming the free boundary problem into the fixed boundary problem

using the

https://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=49418983&type=

https://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=49418950&type=

2.96333337

theory of the parabolic equation and the Schauder fixed point theorem

and combining with the method of function approximation

the existence of the global weak solution of the mathematical model is obtained.

关键词

黑色素瘤反应扩散方程弱解存在性

Keywords

melanomareaction-diffusion equationsweak solutionexistence

references

ASCIERTO P A， KIRKWOOD J M, GROB J J， et al， 2012. The role of BRAF V600 mutation in melanoma［J］. J Transl Med， 10（85）： 1-9.

CUI S， 2005. Global existence of solutions for a free boundary problem modeling the growth of necrotic tumors［J］. Interfaces Free Bound， 7（2）： 147-159.

CUI S， 2015. Introduction to modern theory of partial differential equations［M］. Beijing： Science Press.

FRIEDMAN A， SIEWE N， 2020. Overcoming drug resistance to BRAF inhibitor［J］. Bull Math Biol， 82（1）： 8.

GAFFNEY E A， 2004. The application of mathematical modelling to aspects of adjuvant chemotherapy scheduling［J］. J Math Biol， 48（4）： 375-422.

LADYZENSKAJA O A， SOLONNIKOV V A， URAL'CEVA N N， 1968. Linear and quasi-linear partial differential equations of parabolic type［M］. Providence： American Mathematical Society.

MENZIES A M， LONG G V， 2013. Recent advances in melanoma systemic therapy： BRAF inhibitors， CTLA4 antibodies and beyond［J］. Eur J Cancer， 49（15）： 3229-3241.

SANCHEZ-LAORDEN B，VIROS Ａ，GIROTTI M R， et al， 2014. BRAF inhibitors induce metastasis in RAS mutant or inhibitor-resistant melanoma cells by reactivating MEK and ERK signaling［J］. Sci Signal，7（318）： ra30.

STEINBERG S M， SHABANEH T B， ZHANG P， et al， 2017. Myeloid cells that impair immunotherapy are restored in melanomas with acquired resistance to BRAF inhibitors［J］. Cancer Res， 77（7）： 1599-1610.

WEI X， 2006. Global existence for a free boundary problem modelling the growth of necrotic tumors in the presence of inhibitors［J］. Int J Pure Appl Math， 28（3）： 321-338.

WEI X， GUO C， 2010. Global existence for a mathematical model of the immune response to cancer［J］. Nonlinear Anal Real World Appl， 11（5）： 3903-3911.

XU S， HUANG M， 2014. Global existence and uniqueness of solutions for a free boundary problem modeling the growth of tumors with a necrotic core and a time delay in process of proliferation［J］. Math Probl Eng： 480147.

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