Diffusion and the self-measurability
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&quo...
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| Format: | Article |
| Language: | English |
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University of West Bohemia
2009-06-01
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| Series: | Applied and Computational Mechanics |
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| Online Access: | http://www.kme.zcu.cz/acm/old_acm/full_papers/acm_vol3no1_p05.pdf |
| _version_ | 1831553749815918592 |
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| author | Holeček M. |
| author_facet | Holeček M. |
| author_sort | Holeček M. |
| collection | DOAJ |
| description | 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. |
| first_indexed | 2024-12-17T03:49:55Z |
| format | Article |
| id | doaj.art-1c6d56678fc646bfa39d3d7ffcc7e7e9 |
| institution | Directory Open Access Journal |
| issn | 1802-680X |
| language | English |
| last_indexed | 2024-12-17T03:49:55Z |
| publishDate | 2009-06-01 |
| publisher | University of West Bohemia |
| record_format | Article |
| series | Applied and Computational Mechanics |
| spelling | doaj.art-1c6d56678fc646bfa39d3d7ffcc7e7e92022-12-21T22:04:47ZengUniversity of West BohemiaApplied and Computational Mechanics1802-680X2009-06-01315162Diffusion and the self-measurabilityHoleček M.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.http://www.kme.zcu.cz/acm/old_acm/full_papers/acm_vol3no1_p05.pdfDiffusionSpatial averagingNonlocal thermomechanics |
| spellingShingle | Holeček M. Diffusion and the self-measurability Applied and Computational Mechanics Diffusion Spatial averaging Nonlocal thermomechanics |
| title | Diffusion and the self-measurability |
| title_full | Diffusion and the self-measurability |
| title_fullStr | Diffusion and the self-measurability |
| title_full_unstemmed | Diffusion and the self-measurability |
| title_short | Diffusion and the self-measurability |
| title_sort | diffusion and the self measurability |
| topic | Diffusion Spatial averaging Nonlocal thermomechanics |
| url | http://www.kme.zcu.cz/acm/old_acm/full_papers/acm_vol3no1_p05.pdf |
| work_keys_str_mv | AT holecekm diffusionandtheselfmeasurability |