Tools for stability analysis of fractional reaction diffusion systems
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arXiv
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| Format: | Preprint |
| Published: |
2025
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| _version_ | 1866912461671628800 |
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| 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 |
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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 |