On the non-convexity of solutions in free-boundary problems arising in plasma physics and fluid dynamics

1989 ◽  
Vol 42 (8) ◽  
pp. 1165-1174 ◽  
Author(s):  
Andrew Acker
Keyword(s):  
Fluid Dynamics ◽  
Free Boundary ◽  
Plasma Physics ◽  
Free Boundary Problems ◽  
Boundary Problems

Free boundary problems occurring in planar fluid dynamics

1989 ◽  
Vol 13 (3) ◽  
pp. 285-303 ◽  
Author(s):  
R.P. Gilbert ◽  
Wen Guo-Chun
Keyword(s):  
Fluid Dynamics ◽  
Free Boundary ◽  
Free Boundary Problems ◽  
Boundary Problems

scholarly journals Generic properties of free boundary problems in plasma physics*

Nonlinearity ◽  
2021 ◽  
Vol 35 (1) ◽  
pp. 411-444
Author(s):  
Daniele Bartolucci ◽  
Yeyao Hu ◽  
Aleks Jevnikar ◽  
Wen Yang
Keyword(s):  
Free Boundary ◽  
Plasma Physics ◽  
Free Boundary Problems ◽  
Nonlinear Eigenvalue Problem ◽  
Global Bifurcation ◽  
General Criterion ◽  
Generic Properties ◽  
Model Case ◽  
Boundary Problems ◽  
Boundary Density

Abstract We are concerned with the global bifurcation analysis of positive solutions to free boundary problems arising in plasma physics. We show that in general, in the sense of domain variations, the following alternative holds: either the shape of the branch of solutions resembles the monotone one of the model case of the two-dimensional disk, or it is a continuous simple curve without bifurcation points which ends up at a point where the boundary density vanishes. On the other hand, we deduce a general criterion ensuring the existence of a free boundary in the interior of the domain. Application to a classic nonlinear eigenvalue problem is also discussed.

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