Effective interface conditions for a porous medium type problem
| hal.structure.identifier | Modélisation Mathématique pour l'Oncologie [MONC] | |
| hal.structure.identifier | Institut de Mathématiques de Bordeaux [IMB] | |
| dc.contributor.author | CIAVOLELLA, Giorgia | |
| hal.structure.identifier | Université de Lyon | |
| hal.structure.identifier | Institut Camille Jordan [ICJ] | |
| hal.structure.identifier | Modélisation mathématique, calcul scientifique [MMCS] | |
| dc.contributor.author | DAVID, Noemi | |
| hal.structure.identifier | Université de Lille | |
| hal.structure.identifier | Laboratoire Paul Painlevé - UMR 8524 [LPP] | |
| hal.structure.identifier | Sorbonne Université [SU] | |
| hal.structure.identifier | Laboratoire Jacques-Louis Lions [LJLL (UMR_7598)] | |
| hal.structure.identifier | Modelling and Analysis for Medical and Biological Applications [MAMBA] | |
| dc.contributor.author | POULAIN, Alexandre | |
| dc.date.issued | 2024-02-06 | |
| dc.identifier.issn | 1463-9963 | |
| dc.description.abstractEn | 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 <i>effective interface problem</i>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 <i>a priori<i> 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. | |
| dc.language.iso | en | |
| dc.publisher | European Mathematical Society | |
| dc.subject.en | Membrane boundary conditions | |
| dc.subject.en | Effective interface | |
| dc.subject.en | Porous medium equation | |
| dc.subject.en | Nonlinear reaction-diffusion equations | |
| dc.subject.en | Tumour growth models | |
| dc.title.en | Effective interface conditions for a porous medium type problem | |
| dc.type | Article de revue | |
| dc.identifier.doi | 10.4171/ifb/505 | |
| dc.subject.hal | Mathématiques [math]/Equations aux dérivées partielles [math.AP] | |
| dc.description.sponsorshipEurope | Asymptotic approach to spatial and dynamical organizations | |
| dc.description.sponsorshipEurope | International Doctoral Training in Mathematical Sciences in Paris | |
| bordeaux.journal | Interfaces and Free Boundaries : Mathematical Analysis, Computation and Applications | |
| bordeaux.peerReviewed | oui | |
| hal.identifier | hal-03231456 | |
| hal.version | 1 | |
| hal.popular | non | |
| hal.audience | Internationale | |
| hal.origin.link | https://hal.archives-ouvertes.fr//hal-03231456v1 | |
| bordeaux.COinS | ctx_ver=Z39.88-2004&rft_val_fmt=info:ofi/fmt:kev:mtx:journal&rft.jtitle=Interfaces%20and%20Free%20Boundaries%20:%20Mathematical%20Analysis,%20Computation%20and%20Applications&rft.date=2024-02-06&rft.eissn=1463-9963&rft.issn=1463-9963&rft.au=CIAVOLELLA,%20Giorgia&DAVID,%20Noemi&POULAIN,%20Alexandre&rft.genre=article |
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