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Zbl 0802.65113
Hlaváček, Ivan; Křížek, Michal; Malý, Jan
On Galerkin approximations of a quasilinear nonpotential elliptic problem of a nonmonotone type.
(English)
[J] J. Math. Anal. Appl. 184, No.1, 168-189 (1994). ISSN 0022-247X

This paper deals with a quasilinear problem whose classical formulation reads: Find $u\in C\sp 1(\overline\Omega)$ such that $u\bigl\vert\sb \Omega\in C\sp 2(\Omega)$ and $-\text{div}(A(x,u)\text{grad }u)+ c(x,u)u= f(x,u)$ in $\Omega$, $u= \bar u$ on $\Gamma\sb 1$, $n\sp T A(s,u)\text{grad }u+ \alpha(s,u) u= g(s,u)$ on $\Gamma\sb 2$. 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.
[P.Chocholatý (Bratislava)]
MSC 2000:
*65N30 Finite numerical methods (BVP of PDE)
35J65 (Nonlinear) BVP for (non)linear elliptic equations

Keywords: quasilinear nonpotential elliptic problem; nonmonotone type; Galerkin method; heat conduction problem

Cited in: Zbl 0870.65096

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