具有第三边界坏死核肿瘤数学模型稳态解的存在唯一性  

Existence and uniqueness of the stationary solution of mathematical model of necrotic tumor with the third boundary

作　　者：沈海双 卫雪梅[1] 刘成霞 冯兆永[3] SHEN Haishuang;WEI Xuemei;LIU Chengxia;FENG Zhaoyong(School of Applied Mathematics,Guangdong University of Technology,Guangzhou 510520,China;Stomatological Hospital,Southern Medical University,Guangzhou 510280,China;School of Mathematics,Sun Yat-sen University,Guangzhou 510275,China)

机构地区：[1]广东工业大学应用数学学院,广东广州510520 [2]南方医科大学口腔医院,广东广州510280 [3]中山大学数学学院,广东广州510275

出　　处：《中山大学学报（自然科学版）》2018年第5期140-144,共5页Acta Scientiarum Naturalium Universitatis Sunyatseni

基　　金：国家自然科学基金(11101095);广东省高校特色创新类项目(2016KTSCX028);广东省高层次人才项目(2014011);广东省医学科研基金(A2018339);南方医科大学口腔医院科研培育计划(PY2017017);广州市科技计划项目(201607010144)

摘　　要：研究一个具有第三边界坏死核的肿瘤生长的数学模型,该模型包含了一个抛物型方程和一个常微分方程。假设肿瘤的生长由营养物浓度决定,并且肿瘤形状为球对称。用严格的数学分析的方法,证明了该模型的稳态解的存在唯一性。The mathematical model of necrotic tumor growth with the third boundary is studied.The model comprises a parabolic equation and an ordinary differential equation.The tumor is assumed that the nutrient concentration determines the growth of the tumor which is spherical symmetry.Using the rigorous mathematical analysis method,the existence and uniqueness of the stationary solution of the model are proven.

关 键 词：坏死核肿瘤 第三边界 抛物型方程 稳态解 存在唯一性 

分 类 号：O175[理学—数学]