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Approximation of degenerate parabolic systems by nondegenerate elliptic and parabolic systems. (English) Zbl 0894.65043

Existence of a weak solution is proved for a class of mixed Neumann-Dirichlet problems for a degenerate parabolic system of partial differential equations. The proof is based on a temporal discretization which produces a nondegenerate elliptic system at each time step. It is also shown that if the weak solution is a unique function \(u\), then it is possible to construct a sequence of nondegenerate parabolic systems for which the weak solutions converge to \(u\).

MSC:

65M20 Method of lines for initial value and initial-boundary value problems involving PDEs
35K65 Degenerate parabolic equations
65M60 Finite element, Rayleigh-Ritz and Galerkin methods for initial value and initial-boundary value problems involving PDEs
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