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On Galerkin approximations of a quasilinear nonpotential elliptic problem of a nonmonotone type. (English) Zbl 0802.65113
This paper deals with a quasilinear problem whose classical formulation reads: Find uC 1 (Ω ¯) such that u| Ω C 2 (Ω) and -div(A(x,u)gradu)+c(x,u)u=f(x,u) in Ω, u=u ¯ on Γ 1 , n T A(s,u)gradu+α(s,u)u=g(s,u) on Γ 2 . Precise assumption upon the functions are given. The existence and uniqueness of weak and Galerkin solutions are investigated. A heat conduction problem which describes a temperature distribution in large transformers is presented.

MSC:
65N30Finite elements, Rayleigh-Ritz and Galerkin methods, finite methods (BVP of PDE)
35J65Nonlinear boundary value problems for linear elliptic equations