具有动态边界条件和一般记忆核的Cahn-Hilliard方程全局解的存在唯一性  

Existence and Uniqueness of Global Solution with Dynamic Boundary Conditions and General Memory Kernel for Cahn-Hilliard Equation

作　　者：赵夕雅 蒲志林 罗嘉蓓 ZHAO Xiya;PU Zhilin;LUO Jiabei(School of Mathematical Sciences,Sichuan Normal University,Chengdu Sichuan 610068,China)

机构地区：[1]四川师范大学数学科学学院,成都610068

出　　处：《西华师范大学学报（自然科学版）》2020年第1期71-76,共6页Journal of China West Normal University(Natural Sciences)

基　　金：四川省科技计划项目(2015JY0125)。

摘　　要：主要研究一类具有动态边界条件和一般记忆项的Cahn-Hilliard方程,先将方程写成变分形式,再运用极大单调算子理论证明了局部解的存在唯一性。进一步,用能量不等式证明了能量方程有界且只与初值有关,从而得到全局解的存在唯一性。This paper mainly talks about Cahn-Hilliard equation with dynamic boundary conditions and general memory kernel.Firstly,the equation is written as variational form.Then,the existence and uniqueness of local solution is proved by maximal monotone operator theory.In addition,the existence and uniqueness of global solution is obtained by employing energy inequation to prove that energy equation is bounded and only related to initial value.

关 键 词：动态边界条件 记忆核 极大单调算子 解的存在唯一性 全局解 

分 类 号：O175.2[理学—数学]