Spectral stability analysis of the Dirichlet-to-Neumann map for fractional diffusion equations with a reaction coefficient

Ridha Mdimagh; Fadhel Jday; Ridha Mdimagh; Fadhel Jday

doi:10.3934/math.2024260

AIMS Mathematics

2024, Volume 9, Issue 3: 5394-5406. doi: 10.3934/math.2024260

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Spectral stability analysis of the Dirichlet-to-Neumann map for fractional diffusion equations with a reaction coefficient

Ridha Mdimagh ^{1,3
,
,},
Fadhel Jday ^2,3

1.
Department of Mathematics, College of Science and Arts at Khulis, University of Jeddah, Jeddah, Saudi Arabia
2.
Mathematics Department, Jamoum University College, Umm Al-Qura University, Saudi Arabia
3.
ENIT-LAMSIN, University of Tunis El Manar, Tunisia

Received: 28 September 2023 Revised: 13 January 2024 Accepted: 19 January 2024 Published: 29 January 2024
MSC : 34K20, 35R11, 35S16, 60K50

This paper focused on the stability analysis of the Dirichlet-to-Neumann (DN) map for the fractional diffusion equation with a reaction coefficient $ q $. The main result provided a Hölder-type stability estimate for the map, which was formulated in terms of the Dirichlet eigenvalues and normal derivatives of eigenfunctions of the operator $ A_q : = -\Delta + q $.
- fractional diffusion equation,
- diffusion potential,
- Dirichlet-to-Neumann (DN) map,
- Hölder-type stability,
- spectral decomposition
Citation: Ridha Mdimagh, Fadhel Jday. Spectral stability analysis of the Dirichlet-to-Neumann map for fractional diffusion equations with a reaction coefficient[J]. AIMS Mathematics, 2024, 9(3): 5394-5406. doi: 10.3934/math.2024260

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Abstract

This paper focused on the stability analysis of the Dirichlet-to-Neumann (DN) map for the fractional diffusion equation with a reaction coefficient $ q $. The main result provided a Hölder-type stability estimate for the map, which was formulated in terms of the Dirichlet eigenvalues and normal derivatives of eigenfunctions of the operator $ A_q : = -\Delta + q $.

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