非自治Caputo分数阶发展方程弱解的适定性与不变集  

Invariance Sets and Well-Posedness for the Weak Solution of Non-Autonomous Caputo Fractional Evolution Equation

作　　者：西宣宣 侯咪咪 周先锋[1] Xi Xuanxuan;Hou Mimi;Zhou Xianfeng(School of Mathematical Sciences,Anhui University,Hefei 230039)

机构地区：[1]安徽大学数学科学学院,合肥230039

出　　处：《数学物理学报（A辑）》2021年第1期149-165,共17页Acta Mathematica Scientia

基　　金：国家自然科学基金(11471015,11371027,11601003);安徽省自然科学基金(1508085MA01,1608085MA12,1708085MA15);安徽省高校自然科学研究项目(KJ2016A023)。

摘　　要：该文分析一族含有依赖时间参数t线性算子的时间分数阶非自治发展方程,利用Lions表示定理,得到了弱解适定性的充分条件;基于正交投影,建立了时间分数阶发展方程弱解的不变性准则.该文所研究方程中的算子是依赖时间的.The purpose of this paper is to analyze the time-fractional non-autonomous evolution equation which is associated with a family of linear operators depending on the time parameter t.Using the representation theorem by Lions,we obtain the sufficient conditions for well-posedness of the weak solution.Based on an orthogonal projection,we establish the invariance criterion for the weak solution of the time-fractional evolution equation.The operators of investigated equations are time-dependent.

关 键 词：适定性 CAPUTO分数阶导数 弱解 非自治发展方程 

分 类 号：O175[理学—数学]