Homogenization of a thermo-diffusion system with Smoluchowski interactions

Oleh Krehel; Toyohiko Aiki; Adrian Muntean; Oleh Krehel; Toyohiko Aiki; Adrian Muntean

doi:10.3934/nhm.2014.9.739

Networks and Heterogeneous Media

2014, Volume 9, Issue 4: 739-762. doi: 10.3934/nhm.2014.9.739

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Homogenization of a thermo-diffusion system with Smoluchowski interactions

1.
Department of Mathematics and Computer Science, CASA - Center for Analysis, Scientific computing and Engineering, Eindhoven University of Technology, 5600 MB, PO Box 513, Eindhoven
2.
Department of Mathematical and Physical Sciences, Faculty of Science, Japan Women's University, Tokyo
3.
CASA - Centre for Analysis, Scientific computing and Applications, Department of Mathematics and Computer Science, Institute of Complex Molecular Systems, Eindhoven University of Technology, PO Box 513, 5600 MB Eindhoven

Received: 01 April 2014 Revised: 01 September 2014
Primary: 35B27, 35K59; Secondary: 80M40, 80A25.

We study the solvability and homogenization of a thermal-diffusion reaction problem posed in a periodically perforated domain. The system describes the motion of populations of hot colloidal particles interacting together via Smoluchowski production terms. The upscaled system, obtained via two-scale convergence techniques, allows the investigation of deposition effects in porous materials in the presence of thermal gradients.
- Homogenization,
- well-posedness,
- colloids,
- thermal-diffusion,
- cross-diffusion,
- combustion
Citation: Oleh Krehel, Toyohiko Aiki, Adrian Muntean. Homogenization of a thermo-diffusion system with Smoluchowski interactions[J]. Networks and Heterogeneous Media, 2014, 9(4): 739-762. doi: 10.3934/nhm.2014.9.739

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Abstract

We study the solvability and homogenization of a thermal-diffusion reaction problem posed in a periodically perforated domain. The system describes the motion of populations of hot colloidal particles interacting together via Smoluchowski production terms. The upscaled system, obtained via two-scale convergence techniques, allows the investigation of deposition effects in porous materials in the presence of thermal gradients.

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