一类黑色素瘤耐药机制交叉扩散方程组模型解的存在性  

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

作　　者：陈为 卫雪梅[1] 冯兆永[2] 刘成霞 CHEN Wei;WEI Xuemei;FENG Zhaoyong;LIU Chengxia(School of Applied Mathematics,Guangdong University of Technology,Guangzhou 510520,China;School of Mathematics,Sun Yat-sen University,Guangzhou 510275,China;Stomatological Hospital,Southern Medical University,Guangzhou 510280,China)

机构地区：[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

出　　处：《中山大学学报（自然科学版）（中英文）》2023年第3期137-148,共12页Acta Scientiarum Naturalium Universitatis Sunyatseni

基　　金：Characteristic Innovation Projects of Higher Learning in Guangdong Province(2016KTSCX028);the High-Level Talents Project of Guangdong Province(2014011)。

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Lp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。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 Lp 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 

分 类 号：O175[理学—数学]