The effect of geometry on survival and extinction in a moving-boundary problem motivated by the Fisher–KPP equation

@article{Tam2022TheEO,
  title={The effect of geometry on survival and extinction in a moving-boundary problem motivated by the Fisher–KPP equation},
  author={Alexander K. Y. Tam and Matthew J. Simpson},
  journal={Physica D: Nonlinear Phenomena},
  year={2022}
}

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References

SHOWING 1-10 OF 61 REFERENCES
Revisiting the Fisher–Kolmogorov–Petrovsky–Piskunov equation to interpret the spreading–extinction dichotomy
TLDR
This work revisit travelling wave solutions of the Fisher–KPP model and shows that these results provide new insight into travelling wave solution and the spreading–extinction dichotomy, using a combination of phase plane analysis, perturbation analysis and linearization.
Invading and Receding Sharp-Fronted Travelling Waves
TLDR
The Fisher–Stefan model is studied, which is a generalisation of the Fisher–KPP model obtained by reformulating the Fisher-K PP model as a moving boundary problem, and its analysis has both practical value and an inherent mathematical value.
Hole-closing model reveals exponents for nonlinear degenerate diffusivity functions in cell biology
Extinction of Bistable Populations is Affected by the Shape of their Initial Spatial Distribution
TLDR
This work studies population survival or extinction using a stochastic, discrete lattice-based random walk model where individuals undergo movement, birth and death events and indicates that the shape of the initial spatial distribution of the population affects extinction of bistable populations.
New travelling wave solutions of the Porous–Fisher model with a moving boundary
We examine travelling wave solutions of the Porous-Fisher model, $\partial_t u(x,t)= u(x,t)\left[1-u(x,t)\right] + \partial_x \left[u(x,t) \partial_x u(x,t)\right]$, with a Stefan-like condition at
A REVIEW OF ONE-PHASE HELE-SHAW FLOWS AND A LEVEL-SET METHOD FOR NONSTANDARD CONFIGURATIONS
Abstract The classical model for studying one-phase Hele-Shaw flows is based on a highly nonlinear moving boundary problem with the fluid velocity related to pressure gradients via a Darcy-type law.
Using Experimental Data and Information Criteria to Guide Model Selection for Reaction–Diffusion Problems in Mathematical Biology
TLDR
This work uses Bayesian analysis and information criteria to demonstrate that model selection and model validation should account for both residual errors and model complexity, which are often overlooked in the mathematical biology literature.
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