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Pospíšek, Miroslav

Nonlinear boundary value problems with application to semiconductor device equations. (English) Zbl 0837.65127

Appl. Math., Praha 39, No. 4, 241-258 (1994).
This paper deals with rather general elliptic systems of the form \[ - \sum^N_{j= 1} \partial_j a_{ij}(x, u, \nabla u) a_i(x, u, \nabla u)= f_i \] subject to Dirichlet and (nonlinear) Neumann boundary conditions on different portions of the boundary. This system is a general form of one that arises in the modelling of semiconductor devices. Conditions are given ensuring the well-posedness of the problem in an appropriate weak sense, and the author addresses the convergence of solutions to a Galerkin formulation of the discretized problem.
Reviewer: J.A.Crow (Corvallis)

MSC:

65N30 Finite element, Rayleigh-Ritz and Galerkin methods for boundary value problems involving PDEs
65N12 Stability and convergence of numerical methods for boundary value problems involving PDEs
35J65 Nonlinear boundary value problems for linear elliptic equations
35Q60 PDEs in connection with optics and electromagnetic theory
78A55 Technical applications of optics and electromagnetic theory

Keywords:

Galerkin method; nonlinear Neumann boundary conditions; elliptic systems; semiconductor devices; well-posedness; convergence
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\textit{M. Pospíšek}, Appl. Math., Praha 39, No. 4, 241--258 (1994; Zbl 0837.65127)
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References:

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