Geodesic
Nonlinear boundary value problems with application to semiconductor device equations
Applications of Mathematics, Tome 39 (1994) no. 4, pp. 241-258

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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.
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.
DOI : 10.21136/AM.1994.134255
Classification : 35J65, 65N12, 65N30, 65P05, 78A55
Keywords: boundary value problems for systems of nonlinear elliptic equations; semiconductor device equations; Galerkin method; nonlinear Neumann boundary conditions; elliptic systems; well-posedness; convergence 
Pospíšek, Miroslav. Nonlinear boundary value problems with application to semiconductor device equations. Applications of Mathematics, Tome 39 (1994) no. 4, pp. 241-258. doi: 10.21136/AM.1994.134255
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