TY  - JOUR
ID  - Morales2017
LB  - Morales2017
AU  - Morales, Fernando A.
AU  - Álvarez, Sebastián Naranjo
TI  - The interaction between PDE and graphs in multiscale modeling
ST  - The interaction between PDE and graphs in multiscale modeling
JO  - Opuscula Math.
JA  - Opuscula Math.
JF  - Opuscula Mathematica
PY  - 2017
VL  - 37
IS  - 2
SP  - 327
EP  - 345
DO  - http://dx.doi.org/10.7494/OpMath.2017.37.2.327
UR  - http://dx.doi.org/10.7494/OpMath.2017.37.2.327
AB  - In this article an upscaling model is presented for complex networks with highly clustered regions exchanging/trading quantities of interest at both, microscale and macroscale level. Such an intricate system is approximated by a partitioned open map in \(\mathbb{R}^{2}\) or \(\mathbb{R}^{3}\). The behavior of the quantities is modeled as flowing in the map constructed and thus it is subject to be described using partial differential equations. We follow this approach using the Darcy Porous Media, saturated fluid flow model in mixed variational formulation.
KW  - coupled PDE systems
KW  - mixed formulations
KW  - porous media
KW  - analytic graph theory
KW  - complex networks
SN  - 1232-9274
ER  -