Qualitative bifurcation diagram for Grad-Shafranov type equations

Daniele Bartolucci; Guangze Gu; Aleks Jevnikar; Juncheng Wei; Ruijun Wu

Qualitative bifurcation diagram for Grad-Shafranov type equations

Analysis of PDEs 2026-07-29 v1

Authors: Daniele Bartolucci , Guangze Gu , Aleks Jevnikar , Juncheng Wei , Ruijun Wu

Abstract

We study the qualitative behavior of solutions of Grad-Shafranov type equations arising in plasma physics with general differential operators and general nonlinearities. In particular, we extend recent estimates about threshold values for uniqueness, monotonicity and non-existence of the free boundary. The argument is based on a refined spectral analysis for weighted non-local problems together with comparison techniques and level set analysis.

Keywords

Grad-Shafranov equation bifurcation diagram free boundary spectral analysis comparison principle level set analysis

Cite

@article{arxiv.2607.26861,
  title  = {Qualitative bifurcation diagram for Grad-Shafranov type equations},
  author = {Daniele Bartolucci and Guangze Gu and Aleks Jevnikar and Juncheng Wei and Ruijun Wu},
  journal= {arXiv preprint arXiv:2607.26861},
  year   = {2026}
}

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20 pages