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Diffusion models with microstructure

โœ Scribed by R. E. Showalter

Publisher
Springer Netherlands
Year
1991
Tongue
English
Weight
608 KB
Volume
6
Category
Article
ISSN
0169-3913

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โœฆ Synopsis

Models of diffusion are presented which recognize the local geometry of individual cells or storage sites and the exchange of flux on the micro-scale of these cells. Such models have been obtained by homogenization, but here we indicate stronger existence~uniqueness results of "parabolic" type can be obtained directly. Connections between these models and their historical development will be described.

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โœ A.A. Lacey ๐Ÿ“‚ Article ๐Ÿ“… 1998 ๐Ÿ› Elsevier Science ๐ŸŒ English โš– 710 KB

A number of physical situations, including chemical reactions, electrical heating, and fluid flow, give rise to nonlinear diffusion problems. In this paper models are derived and results relating to the blow-up of the solutions are given. Some of the proofs are outlined and the physical significance