Díaz Díaz, Jesús Ildefonso and Lerena Guil, María Belén and Padial Molina, Juan Francisco (2002) On a nonlocal quasilinear parabolic model related to a current-carrying stellarator. Nonlinear Analysis: Real World Applications, 3 (4). 503 -514. ISSN 1468-1218
Official URL: http://www.sciencedirect.com/science/journal/14681218
An initial-boundary value problem for the nonlinear elliptic–parabolic equation (_(u))t −_u = G(u)(t, x)+J(u)(t, x) is considered. Here _(s) = min(s, 0) = −s−, G and J are nonlocal operators. This problem arises in the study of magnetic confinement of plasma in a stellarator device. An existence theorem of a weak solution defined in this paper is proved. In the course of the proof of the existence theorem with the help of the replacement of _(s) by __(s) = _s+ −s−, a family of regularized parabolic equations is constructed. It is established that the family of solutions of the regularized problems converges as _!0 to the solution of the original initial-boundary value problem. The solvability of the regularized problem with the help of Galerkin’s method is proved.
|Uncontrolled Keywords:||Galerkin method, Current carrying stellarators, Quasilinear nonlocal elliptic parabolic equations, Relative rearrangement|
|Subjects:||Sciences > Mathematics > Differential equations|
|Deposited On:||07 Mar 2011 16:02|
|Last Modified:||07 Mar 2011 16:02|
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