The principal eigenvalue problem for time-periodic nonlocal equations with drift
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arXiv
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| Main Authors: | , , |
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| Format: | Preprint |
| Published: |
2024
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| _version_ | 1866910588449325056 |
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| author | Cloez, Bertrand Abdouni, Adil El Gabriel, Pierre |
| author_facet | Cloez, Bertrand Abdouni, Adil El Gabriel, Pierre |
| contents | In this work, we consider a general time-periodic linear transport equation with integral source term. We prove the existence of a Floquet principal eigenvalue, namely a real number such that the equation rescaled by this number admits nonnegative periodic solutions. We also prove the exponential attractiveness of these solutions. The method relies on general spectral results about positive operators. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2409_01868 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | The principal eigenvalue problem for time-periodic nonlocal equations with drift Cloez, Bertrand Abdouni, Adil El Gabriel, Pierre Analysis of PDEs Functional Analysis Spectral Theory In this work, we consider a general time-periodic linear transport equation with integral source term. We prove the existence of a Floquet principal eigenvalue, namely a real number such that the equation rescaled by this number admits nonnegative periodic solutions. We also prove the exponential attractiveness of these solutions. The method relies on general spectral results about positive operators. |
| title | The principal eigenvalue problem for time-periodic nonlocal equations with drift |
| topic | Analysis of PDEs Functional Analysis Spectral Theory |
| url | https://arxiv.org/abs/2409.01868 |