A priori estimates for minimal surfaces with free boundary, which are not minima of the area

1987 ◽  
Vol 58 (1-2) ◽  
pp. 95-107 ◽  
Author(s):  
Rugang Ye
Keyword(s):  
Free Boundary ◽  
Minimal Surfaces ◽  
A Priori Estimates ◽  
A Priori ◽  
Priori Estimates

A reaction-diffusion-advection competition model with a free boundary

2021 ◽  
Vol 65 (3) ◽  
pp. 25-37
Keyword(s):  
Free Boundary ◽  
A Priori Estimates ◽  
A Priori ◽  
Reaction Diffusion ◽  
Competition Model ◽  
Baseline Data ◽  
The Other ◽  
Quasilinear System ◽  
Priori Estimates ◽  
Competitive Diffusion

In this paper, we study a competitive diffusion quasilinear system with a free boundary. First, we investigate the mathematical questions of the problem. A priori estimates of Schauder type are established, which are necessary for the solvability of the problem. One of two competing species is an invader, which initially exists on a certain sub-interval. The other is initially distributed throughout the area under consideration. Examining the influence of baseline data on the success or failure of the first invasion. We conclude that there is a dichotomy of spread and extinction and give precise criteria for spread and extinction in this model.

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