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Multiple solutions for a free boundary problem arising in plasma physics

Published online by Cambridge University Press:  03 October 2014

Zhongyuan Liu
Zhongyuan Liu*
Affiliation:
School of Mathematics and Information Science, Henan University, Kaifeng, Henan 475004, People's Republic of China, ([email protected])
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Abstract

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.

Type
Research Article
Information
Proceedings of the Royal Society of Edinburgh Section A: Mathematics , Volume 144 , Issue 5 , October 2014 , pp. 965 - 990
Copyright
Copyright © Royal Society of Edinburgh 2014 

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