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Porous Medium Model in Contact with Slow Reservoirs

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From Particle Systems to Partial Differential Equations (PSPDE 2016)

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Abstract

We analyse the hydrodynamic limit of the porous medium model in contact with slow reservoirs which is given by a porous medium equation with Dirichlet, Robin or Neumann boundary conditions depending on the range of the parameter that rules the slowness of the reservoirs.

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References

  1. Baldasso, R., Menezes, O., Neumann, A., Souza, R.R.: Exclusion process with slow boundary. J. Stat. Phys. 167(5), 1112–1142 (2017)

    Article  MathSciNet  Google Scholar 

  2. Bernardin, C., Gonçalves, P., Jiménez-Oviedo, B.: Slow to fast infinitelly extended reservoirs for the symmetric exclusion process with long jumps (2017). arXiv.1702.07216

  3. Feller, W.: An Introduction to a Probability Theory and its Applications. Wiley Series in Probability and Mathematical Statistics, vol. 2 (1970)

    Google Scholar 

  4. Franco, T., Gonçalves, P., Neumann, A.: Phase transition of a heat equation with Robin’s boundary conditions and exclusion process. Trans. Am. Math. Soc. 367(9), 6131–6158 (2013)

    Article  MathSciNet  Google Scholar 

  5. Gonçalves, P., Landim, C., Toninelli, C.: Hydrodynamic limit for a particle system with degenerate rates. Ann. Inst. H. Poincaré: Probab. Stat. 45(4), 887–909 (2009)

    Article  MathSciNet  Google Scholar 

  6. Kipnis, C., Landim, C.: Scaling limits of interacting particle systems. In: Grundlehren der Mathematischen Wissenschaften. Fundamental Principles of Mathematical Sciences, vol. 320. Springer, Berlin (1999)

    Google Scholar 

  7. Muskat, M.: The Flow of Homegeneous Fluids Through Porous Media. McGrawHill, New York (1937)

    MATH  Google Scholar 

  8. Vazquez, J.L.: An introduction to the mathematical theory of the porous medium equation. In: Delfour, M.C., Sabidussi, G. (eds.) Shape Optimization and Free Boundaries, pp. 261–286. Kluwer, Dordrecht (1992)

    Google Scholar 

  9. Vazquez, J.L.: The Porous Medium Equation—Mathematical Theory. Claredon Press, Oxford (2007)

    MATH  Google Scholar 

  10. Zel’dovich, Y.B., Raizer, Y.P.: Physics of Shock Waves and High-Temperature Hydrodynamic Phenomena II. Academic Press, New York (1966)

    Google Scholar 

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Acknowledgements

A. N. was supported through a grant “L’ORÉAL-ABC-UNESCO Para Mulheres na Ciência”. P. G. thanks FCT/Portugal for support through the project UID/MAT/04459/2013. R. P. thanks FCT/Portugal for support through the project Lisbon Mathematics PhD (LisMath). This project has received funding from the European Research Council (ERC) under the European Union’s Horizon 2020 research and innovative programme (grant agreement No 715734).

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Authors and Affiliations

  1. Center for Mathematical Analysis, Geometry and Dynamical Systems, Instituto Superior Técnico, Universidade de Lisboa, Av. Rovisco Pais, 1049-001, Lisboa, Portugal

    Renato de Paula & Patrícia Gonçalves

  2. UFRGS, Instituto de Matemática, Campus do Vale, Av. Bento Gonçalves, 9500. CEP 91509-900, Porto Alegre, Brazil

    Adriana Neumann

Authors
  1. Renato de Paula
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  2. Patrícia Gonçalves
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  3. Adriana Neumann
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Corresponding author

Correspondence to Patrícia Gonçalves .

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Editors and Affiliations

  1. Center for Mathematical Analysis, Geometry and Dynamical Systems, Instituto Superior Técnico, University of Lisbon, Lisbon, Portugal

    Patrícia Gonçalves

  2. Center of Mathematics, University of Minho, Braga, Portugal

    Ana Jacinta Soares

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de Paula, R., Gonçalves, P., Neumann, A. (2018). Porous Medium Model in Contact with Slow Reservoirs. In: Gonçalves, P., Soares, A. (eds) From Particle Systems to Partial Differential Equations . PSPDE 2016. Springer Proceedings in Mathematics & Statistics, vol 258. Springer, Cham. https://doi.org/10.1007/978-3-319-99689-9_7

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