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Effective interface conditions for a porous medium type problem

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  • Additional Information
    • Contributors:
      Laboratoire Jacques-Louis Lions (LJLL (UMR_7598)); Sorbonne Université (SU)-Centre National de la Recherche Scientifique (CNRS)-Université Paris Cité (UPCité); Modelling and Analysis for Medical and Biological Applications (MAMBA); Inria de Paris; Institut National de Recherche en Informatique et en Automatique (Inria)-Institut National de Recherche en Informatique et en Automatique (Inria)-Laboratoire Jacques-Louis Lions (LJLL (UMR_7598)); Sorbonne Université (SU)-Centre National de la Recherche Scientifique (CNRS)-Université Paris Cité (UPCité)-Sorbonne Université (SU)-Centre National de la Recherche Scientifique (CNRS)-Université Paris Cité (UPCité); Dipartimento di Matematica Rome; Università degli Studi di Roma Tor Vergata Roma; Dipartimento di Matematica Bologna; Alma Mater Studiorum Università di Bologna Bologna (UNIBO); Giorgia Ciavolella and Alexandre Poulain have received funding from the European Research Council (ERC) under the European Union’s Horizon 2020 research and innovation programme (grant agreement N° 740623). The work of Giorgio Ciavolella was also partially supported by GNAMPA-INdAM.Noemi David has received funding from the European Union’s Horizon 2020 research and innovation program under the Marie Skłodowska-Curie (grant agreement N° 754362).; European Project: 740623,H2020 Pilier ERC,ADORA(2017); European Project: 754362,MathInParis(2017)
    • Publication Information:
      HAL CCSD
    • Publication Date:
      2023
    • Abstract:
      Motivated by biological applications on tumour invasion through thin membranes, we study a porous-medium type equation where the density of the cell population evolves under Darcy's law, assuming continuity of both the density and flux velocity on the thin membrane which separates two domains. The drastically different scales and mobility rates between the membrane and the adjacent tissues lead to consider the limit as the thickness of the membrane approaches zero. We are interested in recovering the effective interface problem and the transmission conditions on the limiting zero-thickness surface, formally derived by Chaplain et al. (2019), which are compatible with nonlinear generalized Kedem-Katchalsky ones. Our analysis relies on a priori estimates and compactness arguments as well as on the construction of a suitable extension operator which allows to deal with the degeneracy of the mobility rate in the membrane, as its thickness tends to zero.
    • Relation:
      info:eu-repo/grantAgreement//740623/EU/Asymptotic approach to spatial and dynamical organizations/ADORA; info:eu-repo/grantAgreement//754362/EU/International Doctoral Training in Mathematical Sciences in Paris/MathInParis; hal-03231456; https://hal.science/hal-03231456; https://hal.science/hal-03231456v2/document; https://hal.science/hal-03231456v2/file/Porous_membrane_v2.pdf
    • Online Access:
      https://hal.science/hal-03231456
      https://hal.science/hal-03231456v2/document
      https://hal.science/hal-03231456v2/file/Porous_membrane_v2.pdf
    • Rights:
      info:eu-repo/semantics/OpenAccess
    • Accession Number:
      edsbas.6D55DFD5