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
URI: http://www.kme.zcu.cz/acm/old_acm/full_papers/acm_vol3no1_p05.pdf
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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