Title: | Diffusion and the self-measurability |
Authors: | Holeček, Miroslav |
Citation: | Applied and Computational Mechanics. 2009, vol. 3, no. 1, p. 51-62. |
Issue Date: | 2009 |
Publisher: | University of West Bohemia |
Document type: | článek article |
URI: | http://www.kme.zcu.cz/acm/old_acm/full_papers/acm_vol3no1_p05.pdf http://hdl.handle.net/11025/1565 |
ISSN: | 1802-680X (Print) 2336-1182 (Online) |
Keywords: | termomechanika;difúze;parabolické rovnice |
Keywords in different language: | thermomechanics;diffusion;parabolic equations |
Abstract: | The familiar diffusion equation, ∂g/∂t = DΔg, is studied by using the spatially averaged quantities. A non-local relation, so-called the self-measurability condition, fulfilled by this equation is obtained. We define a broad class of diffusion equations defined by some “diffusion inequality”, ∂g/∂t ·Δg ≥ 0, and show that it is equivalent to the self-measurability condition. It allows formulating the diffusion inequality in a non-local form. That represents an essential generalization of the diffusion problem in the case when the field g(x, t) is not smooth. We derive a general differential equation for averaged quantities coming from the self-measurability condition. |
Rights: | © 2009 University of West Bohemia. All rights reserved. |
Appears in Collections: | Volume 3, number 1 (2009) Články / Articles (KME) Volume 3, number 1 (2009) |
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http://hdl.handle.net/11025/1565
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