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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 $$u\in C^ 1(\overline\Omega)$$ such that $$u\bigl|_ \Omega\in C^ 2(\Omega)$$ and $$-\text{div}(A(x,u)\text{grad }u)+ c(x,u)u= f(x,u)$$ in $$\Omega$$, $$u= \bar u$$ on $$\Gamma_ 1$$, $$n^ T A(s,u)\text{grad }u+ \alpha(s,u) u= g(s,u)$$ on $$\Gamma_ 2$$. 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:
 65N30 Finite element, Rayleigh-Ritz and Galerkin methods for boundary value problems involving PDEs 35J65 Nonlinear boundary value problems for linear elliptic equations
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