scholarly journals Geometry and a priori estimates for free boundary problems of the Euler's equation

2008 ◽  
Vol 61 (5) ◽  
pp. 698-744 ◽  
Author(s):  
Jalal Shatah ◽  
Chongchun Zeng
Keyword(s):  
Free Boundary ◽  
A Priori Estimates ◽  
Free Boundary Problems ◽  
A Priori ◽  
Boundary Problems ◽  
Euler’S Equation ◽  
Priori Estimates ◽  
Euler's Equation

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.

On the bifurcation of steady vortex rings from a Green function

1994 ◽  
Vol 116 (3) ◽  
pp. 555-568 ◽  
Author(s):  
Tadie
Keyword(s):  
Green Function ◽  
Free Boundary ◽  
Cross Section ◽  
Free Boundary Problems ◽  
A Priori ◽  
Elliptic Partial Differential Equation ◽  
Vortex Rings ◽  
Boundary Problems ◽  
Bounded Set ◽  
The Green Function

This paper is a supplement to [2]. There, solutions ψ., (μ) of certain free-boundary problems, depending on a small parameter μ, are related to the Green function G., (a(μ)) of a second-order, elliptic, partial differential equation defined on a bounded set Ω ⊂ ℝ2. The free boundary is the boundary of a set A(μ) ⊂ Ω that is unknown a priori and corresponds to the cross-section of a steady vortex ring or of a confined plasma in equilibrium, for example.

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