Local Existence of Solutions of a Free Boundary Problem for Equations of Compressible Viscous Heat-Conducting Capillary Fluids

2000 ◽  
Vol 6 (2) ◽  
Author(s):  
E. Zadrzyńska ◽  
W. M. Zaja̧czkowski
Keyword(s):  
Free Boundary ◽  
Boundary Problem ◽  
Free Boundary Problem ◽  
Existence Of Solutions ◽  
Local Existence ◽  
Heat Conducting ◽  
Viscous Heat ◽  
A Free Boundary Problem ◽  
Local Existence Of Solutions

Multiple solutions for a free boundary problem arising in plasma physics

2014 ◽  
Vol 144 (5) ◽  
pp. 965-990
Author(s):  
Zhongyuan Liu
Keyword(s):  
Free Boundary ◽  
Plasma Physics ◽  
Boundary Problem ◽  
Free Boundary Problem ◽  
Positive Constant ◽  
Multiple Solutions ◽  
Existence Of Solutions ◽  
Image Position ◽  
A Free Boundary Problem ◽  
Outward Unit

In this paper we study the existence of solutions for a free boundary problem arising in the study of the equilibrium of a plasma confined in a tokamak:where p > 2, Ω is a bounded domain in ℝ2, n is the outward unit normal of ∂Ω, α is an unprescribed constant and I is a given positive constant. The set Ω+ = {x ∊ Ω: u(x) > 0} is called a plasma set. Under the condition that the homology of Ω is non-trivial, we show that for any given integer k ≥ 1 there exists λk > 0 such that for λ > λk the problem above has a solution with a plasma set consisting of k components.

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