scholarly journals Variational approach of critical sharp front speeds in degenerate diffusion model with time delay

Nonlinearity ◽  
2020 ◽  
Vol 33 (8) ◽  
pp. 4013-4032
Author(s):  
Tianyuan Xu ◽  
Shanming Ji ◽  
Ming Mei ◽  
Jingxue Yin
Keyword(s):  
Time Delay ◽  
Diffusion Model ◽  
Variational Approach ◽  
Degenerate Diffusion ◽  
Sharp Front

Effect of delay on pattern formation of a Rosenzweig–MacArthur type reaction–diffusion model with spatiotemporal delay

2021 ◽  
Author(s):  
Gao-Xiang Yang ◽  
Xiao-Yu Li
Keyword(s):  
Time Delay ◽  
Diffusion Model ◽  
Reaction Diffusion ◽  
Multiple Scale ◽  
Predator Prey ◽  
Turing Bifurcation ◽  
Reaction Diffusion Model ◽  
Scale Perturbation ◽  
Spatiotemporal Delay ◽  
Theoretical Results

In this paper, a predator–prey reaction–diffusion model with Rosenzweig–MacArthur type functional response and spatiotemporal delay is investigated through using the tool of Turing bifurcation theories. First, by taking the average time delay as a bifurcation parameter, conditions of occurrence of Turing bifurcation are obtained through employing the Routh–Hurwitz criteria. Second, as the average time delay varies the amplitude equations of Turing bifurcation patterns including spots pattern and stripes pattern are also obtained through the multiple scale perturbation method. Finally, the two kinds of spatiotemporal evolution distributions of species such as spots pattern and stripes pattern are shown to illustrate theoretical results.

A Doubly Degenerate Diffusion Model Based on the Gray Level Indicator for Multiplicative Noise Removal

2015 ◽  
Vol 24 (1) ◽  
pp. 249-260 ◽  
Author(s):  
Zhenyu Zhou ◽  
Zhichang Guo ◽  
Gang Dong ◽  
Jiebao Sun ◽  
Dazhi Zhang ◽  
...  
Keyword(s):  
Diffusion Model ◽  
Multiplicative Noise ◽  
Noise Removal ◽  
Degenerate Diffusion ◽  
Gray Level ◽  
Level Indicator ◽  
Model Based ◽  
Multiplicative Noise Removal

scholarly journals Existence and Asymptotic Behavior of Traveling Wave Fronts for a Time-Delayed Degenerate Diffusion Equation

2013 ◽  
Vol 2013 ◽  
pp. 1-20
Author(s):  
Weifang Yan ◽  
Rui Liu
Keyword(s):  
Asymptotic Behavior ◽  
Time Delay ◽  
Diffusion Equation ◽  
Traveling Wave ◽  
Sufficient Conditions ◽  
Degenerate Diffusion ◽  
Wave Fronts ◽  
Traveling Wave Fronts ◽  
Necessary And Sufficient ◽  
Degenerate Diffusion Equation

This paper is concerned with traveling wave fronts for a degenerate diffusion equation with time delay. We first establish the necessary and sufficient conditions to the existence of monotone increasing and decreasing traveling wave fronts, respectively. Moreover, special attention is paid to the asymptotic behavior of traveling wave fronts connecting two uniform steady states. Some previous results are extended.

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