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行波解在一个负的非线性扩散-反应模型中。

Travelling wave solutions in a negative nonlinear diffusion-reaction model.

机构信息

School of Mathematical Sciences, Queensland University of Technology, Brisbane, QLD, Australia.

Biometris, Wageningen University and Research, Wageningen, The Netherlands.

出版信息

J Math Biol. 2020 Dec;81(6-7):1495-1522. doi: 10.1007/s00285-020-01547-1. Epub 2020 Nov 20.

DOI:10.1007/s00285-020-01547-1
PMID:33216181
原文链接:https://pmc.ncbi.nlm.nih.gov/articles/PMC7717045/
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, [Formula: see text], and investigate its relation to the spectral stability of a desingularised linear operator associated with the travelling wave solutions.

摘要

我们使用几何方法证明了在感兴趣的域内具有两次改变符号的凸非线性扩散系数的逻辑动力学非线性扩散反应方程的光滑行波解的存在性。我们确定了最小波速[Formula: see text]，并研究了它与与行波解相关的奇异线性算子的谱稳定性的关系。

https://cdn.ncbi.nlm.nih.gov/pmc/blobs/8047/7717045/0f1309a313ff/285_2020_1547_Fig10_HTML.jpg
https://cdn.ncbi.nlm.nih.gov/pmc/blobs/8047/7717045/15a036c790ec/285_2020_1547_Fig1_HTML.jpg
https://cdn.ncbi.nlm.nih.gov/pmc/blobs/8047/7717045/5c6a50e45a3f/285_2020_1547_Fig2_HTML.jpg
https://cdn.ncbi.nlm.nih.gov/pmc/blobs/8047/7717045/7c3edd47856f/285_2020_1547_Fig3_HTML.jpg
https://cdn.ncbi.nlm.nih.gov/pmc/blobs/8047/7717045/b6c611531b1b/285_2020_1547_Fig4_HTML.jpg
https://cdn.ncbi.nlm.nih.gov/pmc/blobs/8047/7717045/b11bd4ed0a58/285_2020_1547_Fig5_HTML.jpg
https://cdn.ncbi.nlm.nih.gov/pmc/blobs/8047/7717045/3aa1e3dca46c/285_2020_1547_Fig6_HTML.jpg
https://cdn.ncbi.nlm.nih.gov/pmc/blobs/8047/7717045/7ad7078e38bb/285_2020_1547_Fig7_HTML.jpg
https://cdn.ncbi.nlm.nih.gov/pmc/blobs/8047/7717045/75605e774ac4/285_2020_1547_Fig8_HTML.jpg
https://cdn.ncbi.nlm.nih.gov/pmc/blobs/8047/7717045/bc073a482a8d/285_2020_1547_Fig9_HTML.jpg
https://cdn.ncbi.nlm.nih.gov/pmc/blobs/8047/7717045/0f1309a313ff/285_2020_1547_Fig10_HTML.jpg
https://cdn.ncbi.nlm.nih.gov/pmc/blobs/8047/7717045/15a036c790ec/285_2020_1547_Fig1_HTML.jpg
https://cdn.ncbi.nlm.nih.gov/pmc/blobs/8047/7717045/5c6a50e45a3f/285_2020_1547_Fig2_HTML.jpg
https://cdn.ncbi.nlm.nih.gov/pmc/blobs/8047/7717045/7c3edd47856f/285_2020_1547_Fig3_HTML.jpg
https://cdn.ncbi.nlm.nih.gov/pmc/blobs/8047/7717045/b6c611531b1b/285_2020_1547_Fig4_HTML.jpg
https://cdn.ncbi.nlm.nih.gov/pmc/blobs/8047/7717045/b11bd4ed0a58/285_2020_1547_Fig5_HTML.jpg
https://cdn.ncbi.nlm.nih.gov/pmc/blobs/8047/7717045/3aa1e3dca46c/285_2020_1547_Fig6_HTML.jpg
https://cdn.ncbi.nlm.nih.gov/pmc/blobs/8047/7717045/7ad7078e38bb/285_2020_1547_Fig7_HTML.jpg
https://cdn.ncbi.nlm.nih.gov/pmc/blobs/8047/7717045/75605e774ac4/285_2020_1547_Fig8_HTML.jpg
https://cdn.ncbi.nlm.nih.gov/pmc/blobs/8047/7717045/bc073a482a8d/285_2020_1547_Fig9_HTML.jpg
https://cdn.ncbi.nlm.nih.gov/pmc/blobs/8047/7717045/0f1309a313ff/285_2020_1547_Fig10_HTML.jpg

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