Existence and regularity in inverse source problem for fractional reaction-subdiffusion equation perturbed by locally Lipschitz sources

IF 1.3 4区 数学 Q1 MATHEMATICS
T. Tuan
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引用次数: 2

Abstract

In this paper, we consider an inverse problem of determining a space-dependent source in the time fractional reaction-subdiffusion equation involving locally Lipschitz perturbations, where the additional measurements take place at the terminal time which are allowed to be nonlinearly dependent on the state. By providing regularity estimates on both time and space of resolvent operator and using local estimates on Hilbert scales, we establish some results on the existence and uniqueness of solutions and the Lipschitz type stability of solution map of the problem under consideration. In addition, when the input data take more regular values, we obtain results on regularity in time of solution for both the direct linear problem and the inverse problem above.
局部Lipschitz源摄动分数阶反应-扩散方程逆源问题的存在性和正则性
在本文中,我们考虑了在涉及局部Lipschitz扰动的时间分数反应-子扩散方程中确定空间相关源的反问题,其中附加测量发生在允许非线性依赖于状态的终端时间。通过给出求解算子在时间和空间上的正则性估计,并利用Hilbert尺度上的局部估计,得到了该问题解映射的存在唯一性和Lipschitz型稳定性的一些结果。此外,当输入数据取更多的正则值时,我们得到了上述直接线性问题和逆问题在求解时间上的正则性结果。
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来源期刊
Evolution Equations and Control Theory
Evolution Equations and Control Theory MATHEMATICS, APPLIED-MATHEMATICS
CiteScore
3.10
自引率
6.70%
发文量
5
期刊介绍: EECT is primarily devoted to papers on analysis and control of infinite dimensional systems with emphasis on applications to PDE''s and FDEs. Topics include: * Modeling of physical systems as infinite-dimensional processes * Direct problems such as existence, regularity and well-posedness * Stability, long-time behavior and associated dynamical attractors * Indirect problems such as exact controllability, reachability theory and inverse problems * Optimization - including shape optimization - optimal control, game theory and calculus of variations * Well-posedness, stability and control of coupled systems with an interface. Free boundary problems and problems with moving interface(s) * Applications of the theory to physics, chemistry, engineering, economics, medicine and biology
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