The Analysis of Approximate Controllability for Distributed Order Fractional Diffusion Problems
The Analysis of Approximate Controllability for Distributed Order Fractional Diffusion Problems
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DOI：
10.1007/s00245-022-09886-9
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发表时间：
2022-07
影响因子：
1.8
通讯作者：
Li Peng;Yong Zhou
中科院分区：
文献类型：
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作者：
Li Peng;Yong Zhou
为了描述具有时间依赖的数学律衰减的超慢扩散过程，需要建立分布阶分数阶扩散方程。讨论了分数阶拉普拉斯算子在非零外部条件下的分布阶分数扩散问题的外部近似能控性分析。我们首先建立了一些适定性的结果，如解的存在性、唯一性和正则性，允许权函数可以是非连续的。特别地，我们证明了解可以用实值函数积分的级数来表示。在给出伴随系统唯一连续性的基础上，还讨论了系统的近似能控性。
To characterize the ultra-slow diffusion processes with time-dependent logarithmical law attenuation, the distributed order fractional diffusion equation is needed. This paper discusses an analysis of approximate controllability from the exterior of distributed order fractional diffusion problem with the fractional Laplace operator subject to the non-zero exterior condition. We first establish some well-posedness results, such as the existence, uniqueness and regularity of the solutions allowing the weighted functionthat may be non-continuous. Especially, we show that the solutions can be represented by the series for the integral of a real-valued function. After giving the unique continuation property of the adjoint system, approximate controllability of the system is also included.