确定异常扩散方程的扩散浓度和源项

IF 1 4区物理与天体物理 Q3 PHYSICS, MATHEMATICAL

Reports on Mathematical Physics Pub Date : 2024-04-01 DOI:10.1016/S0034-4877(24)00023-5

Asim Ilyas, Salman A. Malik, Kamran Suhaib

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引用次数: 0

摘要

我们考虑的是扩散方程的逆问题，其中涉及空间分数拉普拉奇算子和时间希尔费分数导数，以及迪里希特零边界条件。逆问题是恢复与时间相关的源项和扩散浓度，并附带积分型超定条件。我们讨论了逆问题的解析解，并证明了解析解的存在性和唯一性。我们还为所考虑的逆问题提供了一些特例和示例。

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IDENTIFYING DIFFUSION CONCENTRATION AND SOURCE TERM FOR ANOMALOUS DIFFUSION EQUATION

We consider an inverse problem for diffusion equation involving fractional Laplacian operator in space and Hilfer fractional derivatives in time with Dirichlet zero boundary conditions. The inverse problem is to recover time-dependent source term and diffusion concentration with an integral type over-determination condition. We discuss the analytical solution of the inverse problem and prove the existence and uniqueness of the analytical solution. Some special cases and examples for the considered inverse problem are provided.

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来源期刊

Reports on Mathematical Physics 物理-物理：数学物理

CiteScore

1.80

自引率

0.00%

发文量

审稿时长

6 months

期刊介绍： Reports on Mathematical Physics publish papers in theoretical physics which present a rigorous mathematical approach to problems of quantum and classical mechanics and field theories, relativity and gravitation, statistical physics, thermodynamics, mathematical foundations of physical theories, etc. Preferred are papers using modern methods of functional analysis, probability theory, differential geometry, algebra and mathematical logic. Papers without direct connection with physics will not be accepted. Manuscripts should be concise, but possibly complete in presentation and discussion, to be comprehensible not only for mathematicians, but also for mathematically oriented theoretical physicists. All papers should describe original work and be written in English.