Stochastic homogenization of heat transfer in polycrystals with nonlinear contact conductivities
The heat transfer problem in a polycrystal with nonlinear jump conditions on the grain boundaries will be homogenized using the method of stochastic two-scale convergence developed by Zhikov and Pyatnitskii [V.V. Zhikov and A.L. Pyatnitskii, Homogenization of random singular structures and random me...
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| Format: | Article (Journal) |
| Language: | English |
| Published: |
22 Jun 2011
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| In: |
Applicable analysis
Year: 2012, Volume: 91, Issue: 7, Pages: 1243-1264 |
| ISSN: | 1563-504X |
| DOI: | 10.1080/00036811.2011.567191 |
| Online Access: | Verlag, kostenfrei registrierungspflichtig, Volltext: http://dx.doi.org/10.1080/00036811.2011.567191 Verlag, kostenfrei registrierungspflichtig, Volltext: https://doi.org/10.1080/00036811.2011.567191 
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| Author Notes: | Martin Heida |
| Summary: | The heat transfer problem in a polycrystal with nonlinear jump conditions on the grain boundaries will be homogenized using the method of stochastic two-scale convergence developed by Zhikov and Pyatnitskii [V.V. Zhikov and A.L. Pyatnitskii, Homogenization of random singular structures and random measures, Izv. Math. 70(1) (2006), pp. 19-67] and recently extended by the author [M. Heida, An extension of stochastic two-scale convergence and application, Asympt. Anal. (2010) (in press)]. It will be shown that for monotone Lipschitz jump conditions differentiable in 0, the nonlinearity vanishes in the limit. Additionally, existing Poincaré inequalities will be extended to more general geometric settings with the only restriction of local C 1-interfaces with finite intensity. In particular, the result can now be applied to the Poisson-Voronoi tessellation. |
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| Item Description: | Gesehen am 10.04.2018 |
| Physical Description: | Online Resource |
| ISSN: | 1563-504X |
| DOI: | 10.1080/00036811.2011.567191 |