A free boundary problem and a related semilinear equation

DOI10.1016/0362-546X(80)90004-8zbMath0458.35097OpenAlexW2030430371MaRDI QIDQ3907959

Antonio Ambrosetti, Giovanni Mancini

Publication date: 1980

Published in: Nonlinear Analysis: Theory, Methods & Applications (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/0362-546x(80)90004-8

zbMATH Keywords

Dirichlet problemfree boundary problemsexistence theoremmultiplicity resultbifurcation parameterplasma confinementglobal branch of solutionsTokamak problem

Mathematics Subject Classification ID

Nonlinear elliptic equations (35J60) Statistical mechanics of plasmas (82D10) Free boundary problems for PDEs (35R35) Bifurcations in context of PDEs (35B32)

Related Items (9)

Remarks on the equilibrium shape of a Tokamak plasma ⋮ On the uniqueness and monotonicity of solutions of free boundary problems ⋮ Critical growth for a superlinear elliptic problem in two dimensions ⋮ Some mathematics for quasi-symmetry ⋮ Stability and instability for semilinear parabolic equations with free boundary conditions ⋮ Generic properties of free boundary problems in plasma physics* ⋮ Exact bounds for the radially symmetric shape of confined plasma in the unit circle ⋮ New universal estimates for free boundary problems arising in plasma physics ⋮ On a free boundary problem of plasma equilibria - asymptotic behavior and symmetric property of a solution -

Cites Work

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• A non-linear eigenvalue problem: the shape at equilibrium of a confined plasma
• Elliptic equations with noninvertible Fredholm linear part and bounded nonlinearities
• On a superlinear elliptic boundary value problem
• Some global results for nonlinear eigenvalue problems
• Remarks on a free Boundary Value Problem Arising in Plasma Physics
• Non-uniqueness in the equilibrium shape of a confined plasma^†

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