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Homogenization of a thermal problem with flux jump
1. | Institut Élie Cartan de Lorraine, CNRS, UMR 7502, Université de Lorraine, Metz, 57045, France |
2. | University of Bucharest, Faculty of Physics, Bucharest-Magurele, P.O. Box MG-11, Romania |
References:
[1] |
M. Amar, D. Andreucci and R. Gianni, Evolution and memory effects in the homogenization limit for electrical conduction in biological tissues, Math. Model. Methods Appl. Sci., 14 (2004), 1261-1295.
doi: 10.1142/S0218202504003623. |
[2] |
M. Amar, D. Andreucci, P. Bisegna and R. Gianni, A hierarchy of models for the electrical conduction in biological tissues via two-scale convergence: The nonlinear case, Differ. Integral Equations, 26 (2013), 885-912. |
[3] |
J. L. Auriault, C. Boutin and C. Geindreau, Homogenization of Coupled Phenomena in Heterogenous Media, Wiley, 2010.
doi: 10.1002/9780470612033. |
[4] |
J. L. Auriault and H. Ene, Macroscopic modelling of heat transfer in composites with interfacial thermal barrier, Int. J. of Heat and Mass Transfer, 37 (1994), 2885-2892.
doi: 10.1016/0017-9310(94)90342-5. |
[5] |
A. G. Belyaev, A. L. Pyatnitskiĭ and G. A. Chechkin, Averaging in a perforated domain with an oscillating third boundary condition, Sbornik: Mathematics, 192 (2001), 933-949.
doi: 10.1070/SM2001v192n07ABEH000576. |
[6] |
Y. Benveniste and T. Miloh, Imperfect soft and stiff interfaces in two-dimensional elasticity, Mech. Mater., 33 (2001), 309-323.
doi: 10.1016/S0167-6636(01)00055-2. |
[7] |
D. Brinkman, K. Fellner, P. Markowich and M. T. Wolfram, A drift-diffusion-reaction model for excitonic photovoltaic bilayers: Asymptotic analysis and a 2-D HDG finite element scheme, Math. Models Methods Appl. Sci., 23 (2013), 839-872.
doi: 10.1142/S0218202512500625. |
[8] |
R. Bunoiu and C. Timofte, On the homogenization of a two-permeability problem with flux jump, work in progress. |
[9] |
D. Cioranescu, A. Damlamian, P. Donato, G. Griso and R. Zaki, The periodic unfolding method in domains with holes, SIAM J. Math. Anal., 44 (2012), 718-760.
doi: 10.1137/100817942. |
[10] |
D. Cioranescu, A. Damlamian and G. Griso, The periodic unfolding method in homogenization, SIAM J. Math. Anal., 40 (2008), 1585-1620.
doi: 10.1137/080713148. |
[11] |
D. Cioranescu, P. Donato and R. Zaki, The periodic unfolding method in perforated domains, Portugaliae Math., 63 (2006), 467-496. |
[12] |
D. Cioranescu, P. Donato and R. Zaki, Asymptotic behavior of elliptic problems in perforated domains with nonlinear boundary conditions, Asymptot. Anal., 53 (2007), 209-235. |
[13] |
I. Chourabi and P. Donato, Homogenization and correctors of a class of elliptic problems in perforated domains, Asymptot. Anal., 92 (2015), 1-43. |
[14] |
P. Donato, L. Faella and S. Monsurrò, Homogenization of the wave equation in composites with imperfect interface: a memory effect, J. Math. Pures Appl., 87 (2007), 119-143.
doi: 10.1016/j.matpur.2006.11.004. |
[15] |
P. Donato and K. H. Le Nguyen, Homogenization of diffusion problems with a nonlinear interfacial resistance, Nonlinear Differ. Equ. Appl., 22 (2015), 1345-1380.
doi: 10.1007/s00030-015-0325-2. |
[16] |
P. Donato, K. H. Le Nguyen and R. Tardieu, The periodic unfolding method for a class of imperfect transmission problems, J. Math. Sci. (N. Y.), 176 (2011), 891-927.
doi: 10.1007/s10958-011-0443-2. |
[17] |
P. Donato and S. Monsurrò, Homogenization of two heat conductors with an interfacial contact resistance, Analysis and Applications, 2 (2004), 247-273.
doi: 10.1142/S0219530504000345. |
[18] |
P. Donato and I. Ţenţea, Homogenization of an elastic double-porosity medium with imperfect interface via the periodic unfolding method, Boundary Value Problems, 2013 (2013), 14pp. |
[19] |
H. I. Ene and D. Poliševski, Model of diffusion in partially fissured media, Z. Angew. Math. Phys., 53 (2002), 1052-1059.
doi: 10.1007/PL00013849. |
[20] |
H. I. Ene and C. Timofte, Microstructure models for composites with imperfect interface via the periodic unfolding method, Asymptot. Anal., 89 (2014), 111-122. |
[21] |
H. I. Ene, C. Timofte and I. Ţenţea, Homogenization of a thermoelasticity model for a composite with imperfect interface, Bull. Math. Soc. Sci. Math. Roumanie, 58 (2015), 147-160. |
[22] |
H. I. Ene and C. Timofte, Homogenization results for a dynamic coupled thermoelasticity problem, Romanian Reports in Physics, 68 (2016), 979-989. |
[23] |
K. Fellner and V. Kovtunenko, A discontinuous Poisson-Boltzmann equation with interfacial transfer: Homogenisation and residual error estimate, Applicable Analysis, (2015), 1-22.
doi: 10.1080/00036811.2015.1105962. |
[24] |
M. Gahn, P. Knabner and M. Neuss-Radu, Homogenization of reaction-diffusion processes in a two-component porous medium with a nonlinear flux condition at the interface, and application to metabolic processes in cells, SIAM J. Appl. Math., 76 (2016), 1819-1843.
doi: 10.1137/15M1018484. |
[25] |
Z. Hashin, Thin interphase-imperfect interface in elasticity with application to coated fiber composites, Journal of the Mechanics and Physics of Solids, 50 (2002), 2509-2537.
doi: 10.1016/S0022-5096(02)00050-9. |
[26] |
H. K. Hummel, Homogenization for heat transfer in polycrystals with interfacial resistances, Appl. Anal., 75 (2000), 403-424.
doi: 10.1080/00036810008840857. |
[27] |
E. R. Ijioma, A. Muntean and T. Ogawa, Pattern formation in reverse smouldering combustion: A homogenization approach, Combustion Theory and Modelling, 17 (2013), 185-223.
doi: 10.1080/13647830.2012.734860. |
[28] |
E. C. Jose, Homogenization of a parabolic problem with an imperfect interface, Rev. Roum. Math. Pures Appl., 54 (2009), 189-222. |
[29] |
A. M. Khludnev and V. A. Kovtunenko, Analysis of Cracks in Solids, WIT-Press, Southampton, Boston, 2000. |
[30] |
K. H. Le Nguyen, Homogenization of heat transfer process in composite materials, JEPE, 1 (2015), 175-188. |
[31] |
S. Monsurrò, Homogenization of a two-component composite with interfacial thermal barrier, Adv. Math. Sci. Appl., 13 (2003), 43-63. |
[32] |
D. Polisevski, R. Schiltz-Bunoiu and A. Stanescu, Homogenization cases of heat transfer in structures with interfacial barriers, Bulletin Mathématique de la Société des Sciences Mathématiques de Roumanie, 58 (2015), 463-473. |
[33] |
D. Polisevski and R. Schiltz-Bunoiu, Heat conduction through a first-order jump interface, New Trends in Continuum Mechanics (M. Mihailescu-Suliciu ed.), Theta Series in Advanced Mathematics, 3 (2005), 225-230. |
[34] |
D. Polisevski and R. Schiltz-Bunoiu, Diffusion in an intermediate model of fractured porous media, Bulletin Scientifique, Mathématiques et Informatique, 10 (2004), 99-106. |
[35] |
C. Timofte, Multiscale analysis of diffusion processes in composite media, Computers and Mathematics with Applications, 66 (2013), 1573-1580.
doi: 10.1016/j.camwa.2012.12.003. |
[36] |
C. Timofte, Multiscale modeling of heat transfer in composite materials, Romanian Journal of Physics, 58 (2013), 1418-1427. |
[37] |
C. Timofte, Multiscale analysis in nonlinear thermal diffusion problems in composite structures, Cent. Eur. J. Phys., 8 (2010), 555-561.
doi: 10.2478/s11534-009-0141-6. |
show all references
References:
[1] |
M. Amar, D. Andreucci and R. Gianni, Evolution and memory effects in the homogenization limit for electrical conduction in biological tissues, Math. Model. Methods Appl. Sci., 14 (2004), 1261-1295.
doi: 10.1142/S0218202504003623. |
[2] |
M. Amar, D. Andreucci, P. Bisegna and R. Gianni, A hierarchy of models for the electrical conduction in biological tissues via two-scale convergence: The nonlinear case, Differ. Integral Equations, 26 (2013), 885-912. |
[3] |
J. L. Auriault, C. Boutin and C. Geindreau, Homogenization of Coupled Phenomena in Heterogenous Media, Wiley, 2010.
doi: 10.1002/9780470612033. |
[4] |
J. L. Auriault and H. Ene, Macroscopic modelling of heat transfer in composites with interfacial thermal barrier, Int. J. of Heat and Mass Transfer, 37 (1994), 2885-2892.
doi: 10.1016/0017-9310(94)90342-5. |
[5] |
A. G. Belyaev, A. L. Pyatnitskiĭ and G. A. Chechkin, Averaging in a perforated domain with an oscillating third boundary condition, Sbornik: Mathematics, 192 (2001), 933-949.
doi: 10.1070/SM2001v192n07ABEH000576. |
[6] |
Y. Benveniste and T. Miloh, Imperfect soft and stiff interfaces in two-dimensional elasticity, Mech. Mater., 33 (2001), 309-323.
doi: 10.1016/S0167-6636(01)00055-2. |
[7] |
D. Brinkman, K. Fellner, P. Markowich and M. T. Wolfram, A drift-diffusion-reaction model for excitonic photovoltaic bilayers: Asymptotic analysis and a 2-D HDG finite element scheme, Math. Models Methods Appl. Sci., 23 (2013), 839-872.
doi: 10.1142/S0218202512500625. |
[8] |
R. Bunoiu and C. Timofte, On the homogenization of a two-permeability problem with flux jump, work in progress. |
[9] |
D. Cioranescu, A. Damlamian, P. Donato, G. Griso and R. Zaki, The periodic unfolding method in domains with holes, SIAM J. Math. Anal., 44 (2012), 718-760.
doi: 10.1137/100817942. |
[10] |
D. Cioranescu, A. Damlamian and G. Griso, The periodic unfolding method in homogenization, SIAM J. Math. Anal., 40 (2008), 1585-1620.
doi: 10.1137/080713148. |
[11] |
D. Cioranescu, P. Donato and R. Zaki, The periodic unfolding method in perforated domains, Portugaliae Math., 63 (2006), 467-496. |
[12] |
D. Cioranescu, P. Donato and R. Zaki, Asymptotic behavior of elliptic problems in perforated domains with nonlinear boundary conditions, Asymptot. Anal., 53 (2007), 209-235. |
[13] |
I. Chourabi and P. Donato, Homogenization and correctors of a class of elliptic problems in perforated domains, Asymptot. Anal., 92 (2015), 1-43. |
[14] |
P. Donato, L. Faella and S. Monsurrò, Homogenization of the wave equation in composites with imperfect interface: a memory effect, J. Math. Pures Appl., 87 (2007), 119-143.
doi: 10.1016/j.matpur.2006.11.004. |
[15] |
P. Donato and K. H. Le Nguyen, Homogenization of diffusion problems with a nonlinear interfacial resistance, Nonlinear Differ. Equ. Appl., 22 (2015), 1345-1380.
doi: 10.1007/s00030-015-0325-2. |
[16] |
P. Donato, K. H. Le Nguyen and R. Tardieu, The periodic unfolding method for a class of imperfect transmission problems, J. Math. Sci. (N. Y.), 176 (2011), 891-927.
doi: 10.1007/s10958-011-0443-2. |
[17] |
P. Donato and S. Monsurrò, Homogenization of two heat conductors with an interfacial contact resistance, Analysis and Applications, 2 (2004), 247-273.
doi: 10.1142/S0219530504000345. |
[18] |
P. Donato and I. Ţenţea, Homogenization of an elastic double-porosity medium with imperfect interface via the periodic unfolding method, Boundary Value Problems, 2013 (2013), 14pp. |
[19] |
H. I. Ene and D. Poliševski, Model of diffusion in partially fissured media, Z. Angew. Math. Phys., 53 (2002), 1052-1059.
doi: 10.1007/PL00013849. |
[20] |
H. I. Ene and C. Timofte, Microstructure models for composites with imperfect interface via the periodic unfolding method, Asymptot. Anal., 89 (2014), 111-122. |
[21] |
H. I. Ene, C. Timofte and I. Ţenţea, Homogenization of a thermoelasticity model for a composite with imperfect interface, Bull. Math. Soc. Sci. Math. Roumanie, 58 (2015), 147-160. |
[22] |
H. I. Ene and C. Timofte, Homogenization results for a dynamic coupled thermoelasticity problem, Romanian Reports in Physics, 68 (2016), 979-989. |
[23] |
K. Fellner and V. Kovtunenko, A discontinuous Poisson-Boltzmann equation with interfacial transfer: Homogenisation and residual error estimate, Applicable Analysis, (2015), 1-22.
doi: 10.1080/00036811.2015.1105962. |
[24] |
M. Gahn, P. Knabner and M. Neuss-Radu, Homogenization of reaction-diffusion processes in a two-component porous medium with a nonlinear flux condition at the interface, and application to metabolic processes in cells, SIAM J. Appl. Math., 76 (2016), 1819-1843.
doi: 10.1137/15M1018484. |
[25] |
Z. Hashin, Thin interphase-imperfect interface in elasticity with application to coated fiber composites, Journal of the Mechanics and Physics of Solids, 50 (2002), 2509-2537.
doi: 10.1016/S0022-5096(02)00050-9. |
[26] |
H. K. Hummel, Homogenization for heat transfer in polycrystals with interfacial resistances, Appl. Anal., 75 (2000), 403-424.
doi: 10.1080/00036810008840857. |
[27] |
E. R. Ijioma, A. Muntean and T. Ogawa, Pattern formation in reverse smouldering combustion: A homogenization approach, Combustion Theory and Modelling, 17 (2013), 185-223.
doi: 10.1080/13647830.2012.734860. |
[28] |
E. C. Jose, Homogenization of a parabolic problem with an imperfect interface, Rev. Roum. Math. Pures Appl., 54 (2009), 189-222. |
[29] |
A. M. Khludnev and V. A. Kovtunenko, Analysis of Cracks in Solids, WIT-Press, Southampton, Boston, 2000. |
[30] |
K. H. Le Nguyen, Homogenization of heat transfer process in composite materials, JEPE, 1 (2015), 175-188. |
[31] |
S. Monsurrò, Homogenization of a two-component composite with interfacial thermal barrier, Adv. Math. Sci. Appl., 13 (2003), 43-63. |
[32] |
D. Polisevski, R. Schiltz-Bunoiu and A. Stanescu, Homogenization cases of heat transfer in structures with interfacial barriers, Bulletin Mathématique de la Société des Sciences Mathématiques de Roumanie, 58 (2015), 463-473. |
[33] |
D. Polisevski and R. Schiltz-Bunoiu, Heat conduction through a first-order jump interface, New Trends in Continuum Mechanics (M. Mihailescu-Suliciu ed.), Theta Series in Advanced Mathematics, 3 (2005), 225-230. |
[34] |
D. Polisevski and R. Schiltz-Bunoiu, Diffusion in an intermediate model of fractured porous media, Bulletin Scientifique, Mathématiques et Informatique, 10 (2004), 99-106. |
[35] |
C. Timofte, Multiscale analysis of diffusion processes in composite media, Computers and Mathematics with Applications, 66 (2013), 1573-1580.
doi: 10.1016/j.camwa.2012.12.003. |
[36] |
C. Timofte, Multiscale modeling of heat transfer in composite materials, Romanian Journal of Physics, 58 (2013), 1418-1427. |
[37] |
C. Timofte, Multiscale analysis in nonlinear thermal diffusion problems in composite structures, Cent. Eur. J. Phys., 8 (2010), 555-561.
doi: 10.2478/s11534-009-0141-6. |
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