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- W3036928450 abstract "We consider an extension of the classical Fisher–Kolmogorov equation, called the “Fisher–Stefan” model, which is a moving boundary problem on (0<x<L(t)) . A key property of the Fisher–Stefan model is the “spreading–vanishing dichotomy”, where solutions with (L(t) > L_{textrm{c}}) will eventually spread as (t to infty) , whereas solutions where (L(t) ngtr L_{textrm{c}}) will vanish as (t to infty) . In one dimension it is well known that the critical length is (L_{textrm{c}} = pi/2) . In this work, we re-formulate the Fisher–Stefan model in higher dimensions and calculate (L_{textrm{c}}) as a function of spatial dimensions in a radially symmetric coordinate system. Our results show how (L_{textrm{c}}) depends upon the dimension of the problem, and numerical solutions of the governing partial differential equation are consistent with our calculations. doi: 10.1017/S1446181120000103" @default.
- W3036928450 created "2020-06-25" @default.
- W3036928450 creator A5060813398 @default.
- W3036928450 date "2020-09-02" @default.
- W3036928450 modified "2023-09-25" @default.
- W3036928450 title "Critical length for the spreading-vanishing dichotomy in higher dimensions" @default.
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- W3036928450 doi "https://doi.org/10.21914/anziamj.v62i0.15360" @default.
- W3036928450 hasPublicationYear "2020" @default.
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