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Nonlocal elliptic-parabolic equation arising in the transient regime of a magnetically confined plasma in a Stellarator

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Díaz Díaz, Jesús Ildefonso and Lerena, Belén and Padial Molina, Juan Francisco and Rakotoson, Jean Michel Theresien (1999) Nonlocal elliptic-parabolic equation arising in the transient regime of a magnetically confined plasma in a Stellarator. Comptes Rendus de l'Académie des Sciences. Série I. Mathématique, 329 (9). pp. 773-777. ISSN 0764-4442

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Official URL: http://www.sciencedirect.com/science/article/pii/S0764444299900058


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Abstract

We prove the existence and the regularity of solutions of an elliptic-parabolic equation involving the notions of relative rearrangement and monotone rearrangement. These equations were obtained from 3D MHD systems, taking, (in particular) into account the Ohm and Faraday's laws and the averaging arguments of Hender and Carreras for obtaining a 2D evolution model. Due to the presence of a strong nonlinearity, we introduce a new notion of solution derived from a new property of the relative rearrangement. This allows us to improve the results obtained in the stationnary case by cancelling the condition of smallness of the parameter lambda in the pressure.


Item Type:Article
Uncontrolled Keywords:relative rearrangement; monotone rearrangement; 3D MHD systems
Subjects:Sciences > Mathematics > Functional analysis and Operator theory
Sciences > Mathematics > Differential equations
ID Code:15584
Deposited On:12 Jun 2012 08:20
Last Modified:12 Dec 2018 15:07

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