Variational Approach to Finite-Approximate Controllability of Sobolev-Type Fractional Systems
Variational Approach to Finite-Approximate Controllability of Sobolev-Type Fractional Systems
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DOI：
10.1007/s10957-018-1255-z
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发表时间：
2018-02
影响因子：
1.9
通讯作者：
N. Mahmudov
中科院分区：
文献类型：
--
作者：
N. Mahmudov
在这项工作中，我们扩展了一种变分方法来研究希尔伯特空间中具有非局部条件的 Sobolev 型分数半线性演化方程的有限近似可控性。假设相应的线性方程具有近似可控性，我们得到了Sobolev型分数系统有限近似可控性的充分条件。我们证明，通过一种单独的控制，可以同时获得有限数量约束的近似可控性和精确可达性。所获得的结果是对该问题的最新结果的概括和延续。给出了一个例子作为我们结果的应用。
In this work, we extend a variational approach to study the finite-approximate controllability for Sobolev-type fractional semilinear evolution equations with nonlocal conditions in Hilbert spaces. Assuming the approximate controllability of the corresponding linear equation, we obtain sufficient conditions for the finite-approximate controllability of the Sobolev-type fractional system. We prove that, with one sole control, one can obtain simultaneously approximate controllability and exact reachability of a finite number of constraints. The obtained result is a generalization and continuation of the recent results on this issue. An example is given as an application of our result.