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An algorithm for tracing the boundary curves of mushy regions in some degenerate diffusion problems
Author(s) -
de Mottoni P.,
Santi E.,
Hadeler K.P.
Publication year - 1986
Publication title -
mathematical methods in the applied sciences
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.719
H-Index - 65
eISSN - 1099-1476
pISSN - 0170-4214
DOI - 10.1002/mma.1670080130
Subject(s) - mathematics , degenerate energy levels , boundary (topology) , diffusion , convergence (economics) , dirichlet boundary condition , zero (linguistics) , geodetic datum , mathematical analysis , tracing , boundary value problem , algorithm , physics , computer science , linguistics , philosophy , cartography , quantum mechanics , geography , economics , thermodynamics , economic growth , operating system
We present an algorithm for approximating the solution of the degenerate diffusion problem u t = (ϕ( u )) xx in (0,1) × R + (with zero Dirichlet boundary conditions, and nonnegative initial datum u 0 ), where ϕ( u ) = min { ku 1} for some ϰ > 0. The algorithm also provides an approximation for the interface curves which represent the boundary of the Mushy Region = {( x , t ): ϕ ( u ( x , t )) = 1}. The convergence of the algorithm is proved.