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Gradient bounds for plasma confinement
Author(s) -
Stakgold I.,
Hsiao G. C.
Publication year - 1980
Publication title -
mathematical methods in the applied sciences
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.719
H-Index - 65
eISSN - 1099-1476
pISSN - 0170-4214
DOI - 10.1002/mma.1670020107
Subject(s) - mathematics , plasma , boundary (topology) , point (geometry) , mathematical analysis , maximum principle , interior point method , differential (mechanical device) , boundary value problem , plasma confinement , geometry , mathematical optimization , physics , quantum mechanics , thermodynamics , optimal control
The problem of plasma confinement in a Tokomak machine has recently attracted considerable mathematical attention. In the present article, gradient bounds for the solution are obtained through the use of differential inequalities and the Hopf maximum principle. These estimates, which take slightly different forms in the plasma and vacuum regions, become exact in the one‐dimensional case. An estimate is also given for the distance from the boundary of the interior point where the maximum of the solution is attained.