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

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.