Construction of a Path of MHD Equilibrium Solutions by an Iterative Method

概要

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This paper shows a constructive proof of the existence of a path of solutions to a nonlinear eigenvalue problem expressed by -Δu=λu^+ in Ω, and u=-1 on ∂Ω, where Ω is a two-dimensional domain with a boundary ∂Ω. this problem arises from the ideal MHD equilibria in tori. The existence proof is based on the principle of contraction mappings, which is widely employed in nonlinear problems such as those associated with bifurcation phenomena. Some comments are also given on the application of the present iteration techniques to numerical methods.
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