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Peer-reviewedCC BY-NC-ND 4.0Journal of Functional Analysis

The principal eigenvalue problem for time-periodic nonlocal equations with drift

  • Bertrand Cloez
  • Adil El Abdouni
  • Pierre Gabriel
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Abstract

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.

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Cite

BibTeXRIS
BibTeX
@article{cloez2026principal,
  title = {{The principal eigenvalue problem for time-periodic nonlocal equations with drift}},
  author = {Bertrand Cloez and Adil El Abdouni and Pierre Gabriel},
  journal = {Journal of Functional Analysis},
  year = {2026},
  month = sep,
  eprint = {2409.01868},
  archivePrefix = {arXiv},
  url = {https://hal.science/hal-04690839v2},
  note = {CC BY-NC-ND 4.0},
}
RIS
TY  - JOUR
TI  - The principal eigenvalue problem for time-periodic nonlocal equations with drift
AU  - Bertrand Cloez
AU  - Adil El Abdouni
AU  - Pierre Gabriel
PY  - 2026
DA  - 2026/09/25
JO  - Journal of Functional Analysis
UR  - https://hal.science/hal-04690839v2
AB  - 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.
SN  - 0022-1236
SN  - 1096-0783
ER  -