Travelling wave solutions in a negative nonlinear diffusion–reaction model

Yifei Li; Peter van Heijster; Robert Marangell; Matthew J. Simpson

doi:10.1007/s00285-020-01547-1

Travelling wave solutions in a negative nonlinear diffusion–reaction model

Yifei Li, Peter van Heijster^*, Robert Marangell, Matthew J. Simpson

^*Corresponding author for this work

Research output: Contribution to journal › Article › Academic › peer-review

Abstract

We use a geometric approach to prove the existence of smooth travelling wave solutions of a nonlinear diffusion–reaction equation with logistic kinetics and a convex nonlinear diffusivity function which changes sign twice in our domain of interest. We determine the minimum wave speed, c^∗, and investigate its relation to the spectral stability of a desingularised linear operator associated with the travelling wave solutions.

Original language	English
Pages (from-to)	1495–1522
Journal	Journal of Mathematical Biology
Volume	81
DOIs	https://doi.org/10.1007/s00285-020-01547-1
Publication status	Published - Dec 2020

Keywords

Geometric methods
Nonlinear diffusion
Phase plane analysis
Spectral stability
Travelling wave solutions

Access to Document

10.1007/s00285-020-01547-1Licence: CC BY

https://edepot.wur.nl/536678Licence: CC BY

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Cite this

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title = "Travelling wave solutions in a negative nonlinear diffusion–reaction model",

abstract = "We use a geometric approach to prove the existence of smooth travelling wave solutions of a nonlinear diffusion–reaction equation with logistic kinetics and a convex nonlinear diffusivity function which changes sign twice in our domain of interest. We determine the minimum wave speed, c∗, and investigate its relation to the spectral stability of a desingularised linear operator associated with the travelling wave solutions.",

keywords = "Geometric methods, Nonlinear diffusion, Phase plane analysis, Spectral stability, Travelling wave solutions",

author = "Yifei Li and {van Heijster}, Peter and Robert Marangell and Simpson, {Matthew J.}",

year = "2020",

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T1 - Travelling wave solutions in a negative nonlinear diffusion–reaction model

AU - Li, Yifei

AU - van Heijster, Peter

AU - Marangell, Robert

AU - Simpson, Matthew J.

PY - 2020/12

Y1 - 2020/12

N2 - We use a geometric approach to prove the existence of smooth travelling wave solutions of a nonlinear diffusion–reaction equation with logistic kinetics and a convex nonlinear diffusivity function which changes sign twice in our domain of interest. We determine the minimum wave speed, c∗, and investigate its relation to the spectral stability of a desingularised linear operator associated with the travelling wave solutions.

AB - We use a geometric approach to prove the existence of smooth travelling wave solutions of a nonlinear diffusion–reaction equation with logistic kinetics and a convex nonlinear diffusivity function which changes sign twice in our domain of interest. We determine the minimum wave speed, c∗, and investigate its relation to the spectral stability of a desingularised linear operator associated with the travelling wave solutions.

KW - Geometric methods

KW - Nonlinear diffusion

KW - Phase plane analysis

KW - Spectral stability

KW - Travelling wave solutions

U2 - 10.1007/s00285-020-01547-1

DO - 10.1007/s00285-020-01547-1

M3 - Article

AN - SCOPUS:85096374174

VL - 81

SP - 1495

EP - 1522

JO - Journal of Mathematical Biology

JF - Journal of Mathematical Biology

SN - 0303-6812

ER -