| 非自治Caputo分数阶发展方程弱解的适定性与不变集 |
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| 引用本文： | 西宣宣,侯咪咪,周先锋.非自治Caputo分数阶发展方程弱解的适定性与不变集[J].数学物理学报(A辑),2021(1):149-165. |
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| 作者姓名： | 西宣宣 侯咪咪 周先锋 |
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| 作者单位： | 安徽大学数学科学学院 |
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| 基金项目： | 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)。 |
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| 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.
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| 关 键 词： | 适定性 CAPUTO分数阶导数 弱解 非自治发展方程 |
Invariance Sets and Well-Posedness for the Weak Solution of Non-Autonomous Caputo Fractional Evolution Equation |
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| Xi Xuanxuan,Hou Mimi,Zhou Xianfeng.Invariance Sets and Well-Posedness for the Weak Solution of Non-Autonomous Caputo Fractional Evolution Equation[J].Acta Mathematica Scientia,2021(1):149-165. |
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| Authors: | Xi Xuanxuan Hou Mimi Zhou Xianfeng |
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| Institution: | (School of Mathematical Sciences,Anhui University,Hefei 230039) |
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| Abstract: | 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. |
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| Keywords: | Well-posedness Caputo fractional derivative Weak solution Non-autonomous evolution equation |
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