Effective interface conditions for a porous medium type problem

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Author(s): Ciavolella, Giorgia; David, Noemi; Poulain, Alexandre
Source:
ISSN: 1463-9963 ; EISSN: 1463-9971.
Subject Terms:
Membrane boundary conditions; Effective interface; Porous medium equation; Nonlinear reaction-diffusion equations; Tumour growth models; 2010Mathematics Subject Classification.35B45; 35K57; 35K65; 35Q92; 76N10; 76S05; [MATH.MATH-AP]Mathematics [math]/Analysis of PDEs [math.AP]
Document Type:
article in journal/newspaper
Language:
English

Additional Information
- Contributors:
  Modélisation Mathématique pour l'Oncologie (MONC); Institut de Mathématiques de Bordeaux (IMB); Université Bordeaux Segalen - Bordeaux 2-Université Sciences et Technologies - Bordeaux 1 (UB)-Université de Bordeaux (UB)-Institut Polytechnique de Bordeaux (Bordeaux INP)-Centre National de la Recherche Scientifique (CNRS)-Université Bordeaux Segalen - Bordeaux 2-Université Sciences et Technologies - Bordeaux 1 (UB)-Université de Bordeaux (UB)-Institut Polytechnique de Bordeaux (Bordeaux INP)-Centre National de la Recherche Scientifique (CNRS)-Institut Bergonié Bordeaux; UNICANCER-UNICANCER-Inria Bordeaux - Sud-Ouest; Institut National de Recherche en Informatique et en Automatique (Inria)-Institut National de Recherche en Informatique et en Automatique (Inria); Université Bordeaux Segalen - Bordeaux 2-Université Sciences et Technologies - Bordeaux 1 (UB)-Université de Bordeaux (UB)-Institut Polytechnique de Bordeaux (Bordeaux INP)-Centre National de la Recherche Scientifique (CNRS); Université de Lyon; Institut Camille Jordan (ICJ); École Centrale de Lyon (ECL); Université de Lyon-Université de Lyon-Université Claude Bernard Lyon 1 (UCBL); Université de Lyon-Institut National des Sciences Appliquées de Lyon (INSA Lyon); Université de Lyon-Institut National des Sciences Appliquées (INSA)-Institut National des Sciences Appliquées (INSA)-Université Jean Monnet - Saint-Étienne (UJM)-Centre National de la Recherche Scientifique (CNRS); Modélisation mathématique, calcul scientifique (MMCS); Université de Lyon-Institut National des Sciences Appliquées (INSA)-Institut National des Sciences Appliquées (INSA)-Université Jean Monnet - Saint-Étienne (UJM)-Centre National de la Recherche Scientifique (CNRS)-École Centrale de Lyon (ECL); Université de Lille; Laboratoire Paul Painlevé - UMR 8524 (LPP); Université de Lille-Centre National de la Recherche Scientifique (CNRS); Sorbonne Université (SU); 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); 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
  European Mathematical Society
- Publication Date:
  2024
- Abstract:
  International audience ; 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-03231456v3/document; https://hal.science/hal-03231456v3/file/Submission_final.pdf
- Accession Number:
  10.4171/ifb/505
- Online Access:
  https://doi.org/10.4171/ifb/505
  https://hal.science/hal-03231456
  https://hal.science/hal-03231456v3/document
  https://hal.science/hal-03231456v3/file/Submission_final.pdf
- Rights:
  info:eu-repo/semantics/OpenAccess
- Accession Number:
  edsbas.1A52EF43

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