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arXiv · 2106.04331

Generic properties of free boundary problems in plasma physics

Daniele Bartolucci·Yeyao Hu·Aleks Jevnikar·Wen Yang
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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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Daniele Bartolucci, Yeyao Hu, Aleks Jevnikar, Wen Yang. 2021-06-08. Generic properties of free boundary problems in plasma physics. https://doi.org/10.1088/1361-6544/ac3923

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