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

✍ Scribed by Jesús Ildefonso Díaz; Belén Lerena; Juan Francisco Padial; Jean-Michel Rakotoson

• Publisher: Elsevier Science
• Year: 1999
• Tongue: English
• Weight: 332 KB
• Volume: 329
• Category: Article
• ISSN: 0764-4442
• DOI: 10.1016/s0764-4442(99)90005-8

✦ Synopsis

R&urn&

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 X in the pressure. 0 1999 Acad6mie des sciences&ditions scientifiques et mCdicales Elsevier SAS