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On the singular limit of a two‐phase flow equation with heterogeneities and dynamic capillary pressure
Author(s) -
Kissling F.,
Karlsen K.H.
Publication year - 2014
Publication title -
zamm ‐ journal of applied mathematics and mechanics / zeitschrift für angewandte mathematik und mechanik
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.449
H-Index - 51
eISSN - 1521-4001
pISSN - 0044-2267
DOI - 10.1002/zamm.201200141
Subject(s) - conservation law , limit (mathematics) , dispersion (optics) , diffusion , flow (mathematics) , capillary action , porous medium , convergence (economics) , mechanics , phase (matter) , mathematics , mathematical analysis , capillary pressure , flux (metallurgy) , physics , porosity , materials science , thermodynamics , geology , optics , geotechnical engineering , metallurgy , quantum mechanics , economic growth , economics
We consider conservation laws with spatially discontinuous flux that are perturbed by diffusion and dispersion terms. These equations arise in a theory of two‐phase flow in porous media that includes rate‐dependent (dynamic) capillary pressure and spatial heterogeneities. We investigate the singular limit as the diffusion and dispersion parameters tend to zero, showing strong convergence towards a weak solution of the limit conservation law.