Homogenization of a pseudoparabolic system

Abstract

Pseudoparabolic equations in periodic media are homogenized to obtain upscaled limits by asymptotic expansions and two-scale convergence. The limit is characterized and convergence is established in various linear cases for both the classical binary medium model and the highly heterogeneous case. The limit of vanishing time-delay parameter in either medium is included. The double-porosity limit of Richards' equation with dynamic capillary pressure is obtained.

Keywords:

• homogenization
• pseudoparabolic equations
• fractured porous media
• dynamic capillary pressure

AMS Subject Classifications:

• Primary 35B27
• 35K70
• Secondary 74Q10
• 76S05