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Bistable wavefronts in the Gurtin-MacCamy population model

  • Quentin Griette
  • Franco Herrera
  • Hao Kang
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Abstract

In this paper we prove the existence of monotone traveling wave solutions for an age-structured population model with a monotone and bistable nonlinearity. We formulate the problem in terms of a discrete-time recurrence un+1 = Q[un], with operator Q encoding the role of the speed into its definition. For each speed, we prove the existence of a traveling wave by the general theory of monotone evolution systems, and from appropriate estimates on the speed, we deduce the existence of a traveling wave of the original problem. Also, the sign of the speed is established under an invasion condition, and the asymptotic behavior of the profile is determined by some Tauberian results.

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Cite

BibTeXRIS
BibTeX
@misc{griette2026bistable,
  title = {{Bistable wavefronts in the Gurtin-MacCamy population model}},
  author = {Quentin Griette and Franco Herrera and Hao Kang},
  howpublished = {arXiv},
  year = {2026},
  month = sep,
  doi = {10.48550/arxiv.2609.15853},
  eprint = {2609.15853},
  archivePrefix = {arXiv},
  url = {https://arxiv.org/abs/2609.15853},
}
RIS
TY  - UNPB
TI  - Bistable wavefronts in the Gurtin-MacCamy population model
AU  - Quentin Griette
AU  - Franco Herrera
AU  - Hao Kang
PY  - 2026
DA  - 2026/09/14
PB  - arXiv
DO  - 10.48550/arxiv.2609.15853
UR  - https://arxiv.org/abs/2609.15853
AB  - In this paper we prove the existence of monotone traveling wave solutions for an age-structured population model with a monotone and bistable nonlinearity. We formulate the problem in terms of a discrete-time recurrence u_n+1 = Q[u_n], with operator Q encoding the role of the speed into its definition. For each speed, we prove the existence of a traveling wave by the general theory of monotone evolution systems, and from appropriate estimates on the speed, we deduce the existence of a traveling wave of the original problem. Also, the sign of the speed is established under an invasion condition, and the asymptotic behavior of the profile is determined by some Tauberian results.
ER  -