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PreprintCC BY-NC-SA 4.0arXiv

Propagation rates in integro-differential equations of ignition type

  • Émeric Bouin
  • Jérôme Coville
  • Xi Zhang
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Abstract

This paper provides sharp rates of invasion in nonlinear integro-differential equations of ignition type. The framework covers both integrable convolution kernels and singular fractional-type kernels. While the emergence of a threshold on the decay 1+2s of the jump kernel is expected from earlier works, far fewer quantitative results were available in such a general framework. In particular, in addition to the spreading rates, our study provides information on the shape of the invasion profiles. Importantly, we obtain the first sharp spreading estimate in the critical case s=1/2, which separates linear-in-time and accelerated regimes.

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Cite

BibTeXRIS
BibTeX
@misc{bouin2026propagation,
  title = {{Propagation rates in integro-differential equations of ignition type}},
  author = {Émeric Bouin and Jérôme Coville and Xi Zhang},
  howpublished = {arXiv},
  year = {2026},
  month = aug,
  doi = {10.48550/arxiv.2608.28450},
  eprint = {2608.28450},
  archivePrefix = {arXiv},
  url = {https://arxiv.org/abs/2608.28450},
  note = {CC BY-NC-SA 4.0},
}
RIS
TY  - UNPB
TI  - Propagation rates in integro-differential equations of ignition type
AU  - Émeric Bouin
AU  - Jérôme Coville
AU  - Xi Zhang
PY  - 2026
DA  - 2026/08/28
PB  - arXiv
DO  - 10.48550/arxiv.2608.28450
UR  - https://arxiv.org/abs/2608.28450
AB  - This paper provides sharp rates of invasion in nonlinear integro-differential equations of ignition type. The framework covers both integrable convolution kernels and singular fractional-type kernels. While the emergence of a threshold on the decay 1+2s of the jump kernel is expected from earlier works, far fewer quantitative results were available in such a general framework. In particular, in addition to the spreading rates, our study provides information on the shape of the invasion profiles. Importantly, we obtain the first sharp spreading estimate in the critical case s=1/2, which separates linear-in-time and accelerated regimes.
ER  -