非自治Caputo分数阶发展方程弱解的适定性与不变集

Abstract

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.

Key words: Well-posedness, Caputo fractional derivative, Weak solution, Non-autonomous evolution equation

CLC Number:

O175

Xuanxuan Xi,Mimi Hou,Xianfeng Zhou. Invariance Sets and Well-Posedness for the Weak Solution of Non-Autonomous Caputo Fractional Evolution Equation[J].Acta mathematica scientia,Series A, 2021, 41(1): 149-165.

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

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