The Model Plasma Problem: Existence of a Solution Branch

We are interested in the model plasma problem –u = u⁺in ,u = –d on , _au⁺ dx=j where is a bounded domain in with boundary ; here, j isa given positive number, the function u and the positive number are the unknowns of the problem, and d is a real parameter.Using a variant of the implicit function theorem, we can provethe existence of a global solution branch parametrized by d.The method has the advantage that it can be used for analysingthe approximation of the above problem by a finite-element method.     

Stability of the approximation of a regular solution branch

In this paper we extend the so-called inf-sup conditions tononlinear problems having regular solution branches. The inf-supconditions for nonlinear problems have been introduced, forinstance, by Caloz and Rappaz in 1994. Here we present a moregeneral approach to include turning points on a solution branch.Our abstract results are applied to model examples. E-mail: Gabriel.Caloz{at}univ-rennesl.fr