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.
%0 Journal Article
%1 kissling2013singular
%A Kissling, F.
%A Karlsen, K.H.
%D 2013
%I WILEY-VCH Verlag
%J ZAMM - Journal of Applied Mathematics and Mechanics / Zeitschrift
für Angewandte Mathematik und Mechanik
%K Conservation capillarity, discontinuous dynamic flow flux from:mhartmann function, ians in law, limit, media. porous singular two-phase vorlaeufig
%P n/a--n/a
%R 10.1002/zamm.201200141
%T On the singular limit of a two-phase flow equation with heterogeneities
and dynamic capillary pressure
%U http://dx.doi.org/10.1002/zamm.201200141
%X 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.
@article{kissling2013singular,
abstract = {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.},
added-at = {2018-07-20T10:54:26.000+0200},
author = {Kissling, F. and Karlsen, K.H.},
biburl = {https://puma.ub.uni-stuttgart.de/bibtex/242d1b78569ecd89f80f0f48af825ce75/mathematik},
doi = {10.1002/zamm.201200141},
interhash = {dfd390454fe4506ee81abb066cb2a4d4},
intrahash = {42d1b78569ecd89f80f0f48af825ce75},
issn = {1521-4001},
journal = {ZAMM - Journal of Applied Mathematics and Mechanics / Zeitschrift
f{\"u}r Angewandte Mathematik und Mechanik},
keywords = {Conservation capillarity, discontinuous dynamic flow flux from:mhartmann function, ians in law, limit, media. porous singular two-phase vorlaeufig},
pages = {n/a--n/a},
publisher = {WILEY-VCH Verlag},
timestamp = {2019-12-18T14:37:55.000+0100},
title = {On the singular limit of a two-phase flow equation with heterogeneities
and dynamic capillary pressure},
url = {http://dx.doi.org/10.1002/zamm.201200141},
year = 2013
}