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Research Article | Open Access

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

Ridha Mdimagh1,3( ), Fadhel Jday2,3
Department of Mathematics, College of Science and Arts at Khulis, University of Jeddah, Jeddah, Saudi Arabia
Mathematics Department, Jamoum University College, Umm Al-Qura University, Saudi Arabia
ENIT-LAMSIN, University of Tunis El Manar, Tunisia
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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 := − Δ + q.

Keywords

fractional diffusion equationdiffusion potentialDirichlet-to-Neumann (DN) mapHölder-type stabilityspectral decomposition
CLC number: 34K20, 35R11, 35S16, 60K50

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AIMS Mathematics
Volume 9 Issue 3,
March 2024
Pages 5394-5406
DOI: 10.3934/math.2024260

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Cite this article:
Mdimagh R, Jday F. Spectral stability analysis of the Dirichlet-to-Neumann map for fractional diffusion equations with a reaction coefficient. AIMS Mathematics, 2024, 9(3): 5394-5406. https://doi.org/10.3934/math.2024260

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Received: 28 September 2023
Revised: 13 January 2024
Accepted: 19 January 2024
Published: 15 March 2024
©2024 the Author(s), licensee AIMS Press.

This is an open access article distributed under the terms of the Creative Commons Attribution License (https://creativecommons.org/licenses/by/4.0)