On the singular limit of a two-phase flow equation with heterogeneities
and dynamic capillary pressure
F. Kissling, and K. Karlsen. ZAMM - Journal of Applied Mathematics and Mechanics / Zeitschrift
für Angewandte Mathematik und Mechanik(2013)
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.