Publication Cover
Applicable Analysis
An International Journal
Volume 103, 2024 - Issue 12
27
Views
0
CrossRef citations to date
0
Altmetric
Research Article

Upscaling of a diffusion problem with flux jump in high contrast composites

ORCID Icon &
Pages 2269-2282 | Received 10 Oct 2023, Accepted 02 Dec 2023, Published online: 07 Dec 2023

References

  • Caillerie D, Dinari B. A perturbation problem with two small parametes in the framework of the heat conduction of a fibered reinforced body. Partial Differ Equ. 1987;19:59–78. Warsaw.
  • Bellieud M, Gruais I. Homogenization of an elastic material reinforced by very stiff or heavy fibers. Non local effects. Memory effects. J Math Pures Appl. 2005;84:55–96. doi: 10.1016/j.matpur.2004.02.003
  • Bellieud M. Homogenization of Norton–Hoff fibered composites with high viscosity contrast. SIAM J Math Anal. 2022;54(1):649–692. doi: 10.1137/20M1345785
  • Bellieud M, Bouchitté G. Homogenization of elliptic problems in a fiber reinforced structure. Nonlocal effects. Ann Scuola Norm Sup Pisa Cl Sci (4). 1998;26(3):407–436.
  • Bouchitté G, Bellieud M. Homogenization of a soft elastic material reinforced by fibers. Asymptot Anal. 2002;32:153–183.
  • Boughammoura A. Homogenization of a degenerate parabolic problem in a highly heterogeneous medium with highly anisotropic fibers. Math Comput Model. 2009;49:66–79. doi: 10.1016/j.mcm.2008.07.034
  • Boughammoura A, Braham Y. Homogenization of a three-phase composites of double-porosity type. Czech Math J. 2021;71:45–73. doi: 10.21136/CMJ
  • Murat F, Sili A. A remark about the periodic homogenization of certain composite fibered media. Netw Heterog Media. 2020;15(1):125–142. doi: 10.3934/nhm.2020006
  • Panasenko G. Multi-scale modelling for structures and composites. Springer; 2005.
  • Paroni R, Sili A. Non-local effects by homogenization or 3D-1D dimension reduction in elastic materials reinforced by stiff fibers. J Differ Equ. 2016;260(3):2026–2059. doi: 10.1016/j.jde.2015.09.055
  • Showalter RE. Microstructure models of porous media, homogenization and porous media. Springer; 1997. p. 183–202.
  • Allaire G. Homogenization and two-scale convergence. SIAM J Math Anal. 1992;23:1482–1518. doi: 10.1137/0523084
  • Arbogast T, Douglas Jr. J, Hornung U. Derivation of the double porosity model of single phase flow via homogenization theory. SIAM J Math Anal. 1990;21:823–836. doi: 10.1137/0521046
  • Bakhvalov NS, Panasenko GP. Homogenization: averaging processes in periodic media. Dordrecht/Boston/London: Kluwer; 1989.
  • Bourgeat A, Luckhaus S, Mikelić A. Convergence of the homogenization process for a double-porosity model of immiscible two-phase flow. SIAM J Math Anal. 1996;27:1520–1543. doi: 10.1137/S0036141094276457
  • Bunoiu R, Timofte C. On the homogenization of a two-conductivity problem with flux jump. Commun Math Sci. 2017;15(3):745–763. doi: 10.4310/CMS.2017.v15.n3.a8
  • Bunoiu R, Timofte C. Upscaling of a double porosity problem with jumps in thin porous media. Appl Anal. 2022;101(9):3497–3514. doi: 10.1080/00036811.2020.1854232
  • Gaudiello A, Sili A. Limit models for thin heterogeneous structures with high contrast. J Differ Equ. 2021;302:37–63. doi: 10.1016/j.jde.2021.08.032
  • Donato P, Ţenţea I. Homogenization of an elastic double-porosity medium with imperfect interface via the periodic unfolding method. Bound Value Probl. 2013;2013:265. doi: 10.1186/1687-2770-2013-265
  • Peter MA, Böhm M. Different choices of scaling in homogenization of diffusion and interfacial exchange in a porous medium. Math Methods Appl Sci. 2008;31(11):1257–1282. doi: 10.1002/mma.v31:11
  • Poliševski D. The regularized diffusion in partially fractured porous media. In: Dragos L, editor. Current topics in continuum mechanics II. Bucharest: Academiei Romane; 2003. p. 105–116.
  • De Maio U, Gaudiello A, Sili A. An uncoupled limit model for a high-contrast problem in a thin multi-structure. Atti Accad Naz Lincei Cl Sci Fis Mat Natur. 2022;33(1):39–64. doi: 10.4171/RLM
  • Panasenko GP. Homogenization and multicontinuum models for high contrast composites. IOP Conf Ser Mater Sci Eng. 2019;683:012020. doi: 10.1088/1757-899X/683/1/012020
  • Sili A. On the limit spectrum of a degenerate operator in the framework of periodic homogenization or singular perturbation problems. C R Math. 2022;360:1–23.
  • Amar M, Gianni R. Laplace–Beltrami operator for the heat conduction in polymer coating of electronic devices. Discrete Cont Dyn Syst Ser B. 2018;23(4):1739–1756.
  • Amar M, Andreucci D, Gianni R, et al. Concentration and homogenization in electrical conduction in heterogeneous media involving the Laplace–Beltrami operator. Calc Var. 2020;59:99. doi: 10.1007/s00526-020-01749-x
  • Amar M, Andreucci D, Timofte C. Heat conduction in composite media involving imperfect contact and perfectly conductive inclusions. Math Methods Appl Sci. 2022;45(17):11355–11379. doi: 10.1002/mma.v45.17
  • Amar M, Andreucci D, Timofte C. Interface potential in composites with general imperfect transmission conditions. Z Angew Math Phys. 2023;74:200. doi: 10.1007/s00033-023-02094-7
  • Bunoiu R, Ramdani K, Timofte C. Homogenization of a transmission problem with sign-changing coefficients and interfacial flux jump. Commun Math Sci. 2023;21(7):2029–2049. doi: 10.4310/cms.2023.v21.n7.a13
  • Bunoiu R, Timofte C. Homogenization of a thermal problem with flux jump. Netw Heterog Media. 2016;11(4):545–562. doi: 10.3934/nhm
  • Bunoiu R, Timofte C. Diffusion problems in composite media with interfacial flux jump. Rom Rep Phys. 2018;70:116.
  • Bunoiu R, Timofte C. Upscaling of a diffusion problem with interfacial flux jump leading to a modified Barenblatt model. ZAMM. 2019;99(2):e201800018. doi: 10.1002/zamm.v99.2
  • Fatima T, Ijioma E, Ogawa T, et al. Homogenization and dimension reduction of filtration combustion in heterogeneous thin layers. Netw Heterog Media. 2014;9(4):709–737. doi: 10.3934/nhm.2014.9.709
  • Gahn M, Neuss-Radu M, Knabner P. Homogenization of reaction-diffusion processes in a two-component porous medium with nonlinear flux conditions at the interface. SIAM J Appl Math. 2016;76:1819–1843. doi: 10.1137/15M1018484
  • Gahn M, Neuss-Radu M, Knabner P. Effective interface conditions for processes through thin heterogeneous layers with nonlinear transmission at the microscopic bulk-layer interface. Netw Heterog Media. 2018;13:609–640. doi: 10.3934/nhm.2018028
  • Ijioma ER, Muntean A, Ogawa T. Pattern formation in reverse smouldering combustion: a homogenization approach. Combust Theory Model. 2013;17:185–223. doi: 10.1080/13647830.2012.734860
  • Neuss-Radu M, Jäger W. Effective transmission conditions for reaction-diffusion processes in domains separated by an interface. SIAM J Math Anal. 2007;39:687–720. doi: 10.1137/060665452
  • Allaire G, Habibi Z. Homogenization of a conductive, convective and radiative heat transfer problem in a heterogeneous domain. SIAM J Math Anal. 2013;45:1136–1178. doi: 10.1137/110849821
  • Cioranescu D, Damlamian A, Griso G. The periodic unfolding method. Singapore: Springer; 2018. (Theory and applications to partial differential problems. Series in contemporary mathematics; 3).
  • Donato P, Le Nguyen KH, Tardieu R. The periodic unfolding method for a class of imperfect transmission problems. J Math Sci (N Y). 2011;176(6):891–927. doi: 10.1007/s10958-011-0443-2

Reprints and Corporate Permissions

Please note: Selecting permissions does not provide access to the full text of the article, please see our help page How do I view content?

To request a reprint or corporate permissions for this article, please click on the relevant link below:

Academic Permissions

Please note: Selecting permissions does not provide access to the full text of the article, please see our help page How do I view content?

Obtain permissions instantly via Rightslink by clicking on the button below:

If you are unable to obtain permissions via Rightslink, please complete and submit this Permissions form. For more information, please visit our Permissions help page.