scholarly journals Existence and instability of some nontrivial steady states for the SKT competition model with large cross diffusion

2020 ◽  
Vol 40 (6) ◽  
pp. 3657-3682
Author(s):  
Qing Li ◽  
◽  
Yaping Wu ◽  
Keyword(s):  
Competition Model ◽  
Steady States ◽  
Cross Diffusion

scholarly journals Stability of patterns and of constant steady states for a cross-diffusion system

2016 ◽  
Vol 293 ◽  
pp. 208-216 ◽  
Author(s):  
G. Svantnerné Sebestyén ◽  
István Faragó ◽  
Róbert Horváth ◽  
R. Kersner ◽  
M. Klincsik
Keyword(s):  
Steady States ◽  
Diffusion System ◽  
Cross Diffusion

scholarly journals A Lotka-Volterra Competition Model with Cross-Diffusion

2013 ◽  
Vol 2013 ◽  
pp. 1-5
Author(s):  
Wenyan Chen ◽  
Ya Chen
Keyword(s):  
Boundary Condition ◽  
Positive Solutions ◽  
Dirichlet Boundary Condition ◽  
Dirichlet Boundary ◽  
Upper And Lower Solutions ◽  
Sufficient Conditions ◽  
Competition Model ◽  
Homogeneous Dirichlet Boundary Condition ◽  
Cross Diffusion ◽  
Existence Of Positive Solutions

A Lotka-Volterra competition model with cross-diffusions under homogeneous Dirichlet boundary condition is considered, where cross-diffusions are included in such a way that the two species run away from each other because of the competition between them. Using the method of upper and lower solutions, sufficient conditions for the existence of positive solutions are provided when the cross-diffusions are sufficiently small. Furthermore, the investigation of nonexistence of positive solutions is also presented.

scholarly journals Positive steady states of a ratio-dependent predator-prey system with cross-diffusion

2019 ◽  
Vol 16 (6) ◽  
pp. 6753-6768
Author(s):  
Xiaoling Li ◽  
◽  
Guangping Hu ◽  
Xianpei Li ◽  
Zhaosheng Feng ◽  
...  
Keyword(s):  
Steady States ◽  
Predator Prey ◽  
Cross Diffusion ◽  
Prey System ◽  
Positive Steady States ◽  
Ratio Dependent
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