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boundary value problems for systems of nonlinear elliptic equations; semiconductor device equations; Galerkin method; nonlinear Neumann boundary conditions; elliptic systems; well-posedness; convergence
The paper deals with boundary value problems for systems of nonlinear elliptic equations in a relatively general form. Theorems based on monotone operator theory and concerning the existence of weak solutions of such a system, as well as the convergence of discretized problem solutions are presented. As an example, the approach is applied to the stationary Van Roosbroeck’s system, arising in semiconductor device modelling. A convergent algorithm suitable for solving sets of algebraic equations generated by the discretization procedure proposed will be described in a forthcoming paper.
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