Inverse coefficient problems for the heat equation with fractional Laplacian

Azizbek Mamanazarov; Durvudkhan Suragan

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arXiv · 2405.13338

Inverse coefficient problems for the heat equation with fractional Laplacian

Azizbek Mamanazarov·Durvudkhan Suragan

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Abstract

In the present paper we study inverse problems related to determining the time-dependent coefficient and unknown source function of fractional heat equations. Our approach shows that having just one set of data at an observation point ensures the existence of a weak solution for the inverse problem. Furthermore, if there is an additional datum at the observation point, it leads to a specific formula for the time-dependent source coefficient. Moreover, we investigate inverse problems involving non-local data and recovering the space-dependent source function of the fractional heat equation.

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Azizbek Mamanazarov, Durvudkhan Suragan. 2024-05-22. Inverse coefficient problems for the heat equation with fractional Laplacian. https://arxiv.org/abs/2405.13338

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