Asymptotic Behavior and Error Bounds for Fisher-KPP Equations on the Real Half-Line

Abstract

We study the Fisher--KPP equation on the half-line under Dirichlet,Neumann, and Robin boundary conditions. For the autonomous logistic equation, we identify bounded stationary profiles converging to $1$ and obtain exponential far-field comparison estimates. We prove local uniform convergence of nontrivial Neumann solutions to $1$. Assuming local uniform convergence of the Robin solution to its stationary profile, we derive asymptotic Neumann--Robin comparison estimates. We then consider small time-periodic Neumann and Robin boundary forcing. Under exponential stability of the homogeneous linearized semigroup, we construct a locally unique small periodic lifted mild solution and obtain a first-order expansion with a uniform O(ε²) remainder in C₀([0,∞)).

Logarithmic upper bounds and axial front selection for spatially periodic lattice Fisher--KPP equations
Yuanyang Hu, Zhenkun Wang
arXiv5 Oct 2026PreprintCC BY 4.0Full textAnalysis & PDEsarXiv
Quantitative asymptotic error analysis and Richardson extrapolation for exponential Euler approximations of stochastic wave equations
Jianbo Cui, Diancong Jin, Huagui Liu +1
arXiv12 Oct 2026PreprintarXiv licenceFull textNumerical analysis & scientific computingarXiv
Radial-type error bounds for semidefinite feasibility problems without strict feasibility: qualitative estimates and asymptotic tightness
Mitsuhiro Nishijima, Guoyin Li, Bruno F. Lourenço
arXiv28 Aug 2026PreprintarXiv licenceFull textOptimisation & controlarXiv
Asymptotic behavior of bounded Mild Solutions to some fractional differential equations involving the ψ-Hilfer derivative
Adama Kabore, Pihiré Vincent Ouena, Moumini Kéré +1
HAL24 Sep 2026PreprintCC BY-NC-SA 4.0Full textGeneral mathematicsHAL
uniqueness and asymptotic behavior of the stationary Navier-Stokes equations in a slab
Han Li, Jingwen Han
arXiv29 Aug 2026PreprintarXiv licenceFull textAnalysis & PDEsarXiv

Cite

BibTeX RIS

BibTeX

@misc{chu2026asymptotic,
  title = {{Asymptotic Behavior and Error Bounds for Fisher-KPP Equations on the Real Half-Line}},
  author = {Chu Chu and M. W. Wong},
  howpublished = {arXiv},
  year = {2026},
  month = oct,
  doi = {10.48550/arxiv.2608.12379},
  eprint = {2608.12379},
  archivePrefix = {arXiv},
  url = {https://arxiv.org/abs/2608.12379},
}

RIS

TY  - UNPB
TI  - Asymptotic Behavior and Error Bounds for Fisher-KPP Equations on the Real Half-Line
AU  - Chu Chu
AU  - M. W. Wong
PY  - 2026
DA  - 2026/10/03
PB  - arXiv
DO  - 10.48550/arxiv.2608.12379
UR  - https://arxiv.org/abs/2608.12379
AB  - We study the Fisher--KPP equation on the half-line under Dirichlet,Neumann, and Robin boundary conditions. For the autonomous logistic equation, we identify bounded stationary profiles converging to $1$ and obtain exponential far-field comparison estimates. We prove local uniform convergence of nontrivial Neumann solutions to $1$. Assuming local uniform convergence of the Robin solution to its stationary profile, we derive asymptotic Neumann--Robin comparison estimates. We then consider small time-periodic Neumann and Robin boundary forcing. Under exponential stability of the homogeneous linearized semigroup, we construct a locally unique small periodic lifted mild solution and obtain a first-order expansion with a uniform O(ε^2) remainder in C_0([0,∞)).
ER  -

Abstract

Related

Cite