Tools for stability analysis of fractional reaction diffusion systems

Fuente: arXiv
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Main Authors: Ahmad, Sofwah, Cygan, Szymon, Karch, Grzegorz
Format: Preprint
Published: 2025
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_version_ 1866912461671628800
author Ahmad, Sofwah
Cygan, Szymon
Karch, Grzegorz
author_facet Ahmad, Sofwah
Cygan, Szymon
Karch, Grzegorz
contents The linearization principle states that the stability (or instability) of solutions to a suitable linearization of a nonlinear problem implies the stability (or instability) of solutions to the original nonlinear problem. In this work, we prove this principle for solutions of abstract fractional reaction-diffusion equations with a fractional derivative in time of order $α\in (0,1)$. Then, we apply these results to particular fractional reaction-diffusion equations, obtaining, for example, the counterpart of the classical Turing instability in the case of fractional equations.
format Preprint
id arxiv_https___arxiv_org_abs_2507_02094
institution arXiv
publishDate 2025
record_format arxiv
spellingShingle Tools for stability analysis of fractional reaction diffusion systems
Ahmad, Sofwah
Cygan, Szymon
Karch, Grzegorz
Analysis of PDEs
35R11, 35B35, 35K57, 35B40, 34G20
The linearization principle states that the stability (or instability) of solutions to a suitable linearization of a nonlinear problem implies the stability (or instability) of solutions to the original nonlinear problem. In this work, we prove this principle for solutions of abstract fractional reaction-diffusion equations with a fractional derivative in time of order $α\in (0,1)$. Then, we apply these results to particular fractional reaction-diffusion equations, obtaining, for example, the counterpart of the classical Turing instability in the case of fractional equations.
title Tools for stability analysis of fractional reaction diffusion systems
topic Analysis of PDEs
35R11, 35B35, 35K57, 35B40, 34G20
url https://arxiv.org/abs/2507.02094