In 2D, large-current plasma equilibria either vanish or form finite collections of spikes of three types (Dancer-Yan, 'Type II', and fading), with quantized sizes and locations governed by a Hamiltonian condition.
Simplicity and boundary behavior of spike sequences for a superlinear problem in plasma physics
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We prove that spike sequences related to a nonlinear problem of Grad-Shafranov type are always simple and always converge toward interior points of the domain. This sharpens the blow-up analysis carried out by Bartolucci-Jevnikar-Wu [Calc. Var. 2025] and provides a converse to the existence result for spike sequences obtained by Wei [Proc. Edinb. Math. Soc. 2001].
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Classification of singular limits for free boundary and singularly perturbed elliptic problems: the Dancer-Yan spikes revisited
In 2D, large-current plasma equilibria either vanish or form finite collections of spikes of three types (Dancer-Yan, 'Type II', and fading), with quantized sizes and locations governed by a Hamiltonian condition.