论文标题
Banach空间中非自主演化方程的近似可控性
Approximate controllability of a non-autonomous evolution equation in Banach spaces
论文作者
论文摘要
在本文中，我们考虑了可分离的，反射性的Banach空间中的非自治非线性进化方程。首先，我们考虑一个线性问题，并通过在最佳控制问题的帮助下找到反馈控制来确定近似可控性结果。然后，我们使用线性进化系统的理论，分辨率运算符的属性和Schauder的固定点定理，为BANACH空间中的半线性微分方程建立了近似可控性结果。最后，我们提供了Banach空间中非自治的非线性扩散方程的示例，以验证我们获得的结果。
In this paper, we consider a non-autonomous nonlinear evolution equation in separable, reflexive Banach spaces. First, we consider a linear problem and establish the approximate controllability results by finding a feedback control with the help of an optimal control problem. We then establish the approximate controllability results for a semilinear differential equation in Banach spaces using the theory of linear evolution systems, properties of resolvent operator and Schauder's fixed point theorem. Finally, we provide an example of a non-autonomous, nonlinear diffusion equation in Banach spaces to validate the results we obtained.
