# A Global Solution Curve for a Class of Free Boundary Value Problems Arising in Plasma Physics

A Global Solution Curve for a Class of Free Boundary Value Problems Arising in Plasma Physics We study the existence and multiplicity of solutions and the global solution curve of the following free boundary value problem, arising in plasma physics, see Temam (Arch Ration Mech Anal 60(1):51–73, 1975–1976 ), and Berestycki and Brezis (Nonlinear Anal. 4(3):415–436, 1980 ): find a function $$u(x)$$ u ( x ) and a constant $$b$$ b , satisfying \begin{aligned}&\Delta u+g(x,u)=p(x) \; \;\text{ in }\, D \\&u \,| \, _{\partial D}=b, \; \;\; \;\int \limits _{\partial D} \frac{\partial u}{\partial n} \, ds=0. \end{aligned} Δ u + g ( x , u ) = p ( x ) in D u | ∂ D = b , ∫ ∂ D ∂ u ∂ n d s = 0 . Here $$D \subset R^n$$ D ⊂ R n , is a bounded domain, with a smooth boundary. This problem can be seen as a PDE generalization of the periodic problem for one-dimensional pendulum-like equations. We use continuation techniques. Our approach is suitable for numerical computations. http://www.deepdyve.com/assets/images/DeepDyve-Logo-lg.png Applied Mathematics and Optimization Springer Journals

# A Global Solution Curve for a Class of Free Boundary Value Problems Arising in Plasma Physics

, Volume 71 (1) – Feb 1, 2015
14 pages
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Publisher
Springer US
Copyright
Copyright © 2015 by Springer Science+Business Media New York
Subject
Mathematics; Calculus of Variations and Optimal Control; Optimization; Systems Theory, Control; Theoretical, Mathematical and Computational Physics; Mathematical Methods in Physics; Numerical and Computational Physics
ISSN
0095-4616
eISSN
1432-0606
D.O.I.
10.1007/s00245-014-9251-7
Publisher site
See Article on Publisher Site

### Abstract

We study the existence and multiplicity of solutions and the global solution curve of the following free boundary value problem, arising in plasma physics, see Temam (Arch Ration Mech Anal 60(1):51–73, 1975–1976 ), and Berestycki and Brezis (Nonlinear Anal. 4(3):415–436, 1980 ): find a function $$u(x)$$ u ( x ) and a constant $$b$$ b , satisfying \begin{aligned}&\Delta u+g(x,u)=p(x) \; \;\text{ in }\, D \\&u \,| \, _{\partial D}=b, \; \;\; \;\int \limits _{\partial D} \frac{\partial u}{\partial n} \, ds=0. \end{aligned} Δ u + g ( x , u ) = p ( x ) in D u | ∂ D = b , ∫ ∂ D ∂ u ∂ n d s = 0 . Here $$D \subset R^n$$ D ⊂ R n , is a bounded domain, with a smooth boundary. This problem can be seen as a PDE generalization of the periodic problem for one-dimensional pendulum-like equations. We use continuation techniques. Our approach is suitable for numerical computations.

### Journal

Applied Mathematics and OptimizationSpringer Journals

Published: Feb 1, 2015

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