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Convergence rates to traveling waves for an FKPP model with nonlinear advection

  • Ryan Patterson
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Abstract

We establish convergence rates of solutions to traveling waves for a reaction diffusion model with nonlinear advection. The convergence rate is proven using the shape defect function. We introduce a novel energy methods-based approach that uses a weighted Nash inequality to obtain L∞-estimates on the shape defect function. In determining the convergence rates, we also establish the front location for the model.

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Cite

BibTeXRIS
BibTeX
@misc{patterson2026convergence,
  title = {{Convergence rates to traveling waves for an FKPP model with nonlinear advection}},
  author = {Ryan Patterson},
  howpublished = {arXiv},
  year = {2026},
  month = sep,
  doi = {10.48550/arxiv.2609.03084},
  eprint = {2609.03084},
  archivePrefix = {arXiv},
  url = {https://arxiv.org/abs/2609.03084},
}
RIS
TY  - UNPB
TI  - Convergence rates to traveling waves for an FKPP model with nonlinear advection
AU  - Ryan Patterson
PY  - 2026
DA  - 2026/09/21
PB  - arXiv
DO  - 10.48550/arxiv.2609.03084
UR  - https://arxiv.org/abs/2609.03084
AB  - We establish convergence rates of solutions to traveling waves for a reaction diffusion model with nonlinear advection. The convergence rate is proven using the shape defect function. We introduce a novel energy methods-based approach that uses a weighted Nash inequality to obtain L^∞-estimates on the shape defect function. In determining the convergence rates, we also establish the front location for the model.
ER  -