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Multi-species viscous models for tissue growth: incompressible limit and qualitative behaviour

Abstract : We introduce two 2D mechanical models reproducing the evolution of two viscous tissues in contact. Their main property is to model the swirling cell motions while keeping the tissues segregated, as observed during vertebrate embryo elongation. Segregation is encoded differently in the two models: by passive or active segregation (based on a mechanical repulsion pressure). We compute the incompressible limits of the two models, and obtain strictly segregated solutions. The two models thus obtained are compared. A striking feature in the active segregation model is the persistence of the repulsion pressure at the limit: a ghost effect is discussed and confronted to the biological data. Thanks to a transmission problem formulation at the incompressible limit, we show a pressure jump at the tissues' boundaries.
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https://hal.archives-ouvertes.fr/hal-03618303
Contributor : Pierre Degond Connect in order to contact the contributor
Submitted on : Thursday, August 4, 2022 - 4:16:41 PM
Last modification on : Friday, August 5, 2022 - 12:02:00 PM

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Pierre Degond, Sophie Hecht, Michèle Romanos, Ariane Trescases. Multi-species viscous models for tissue growth: incompressible limit and qualitative behaviour. Journal of Mathematical Biology, Springer Verlag (Germany), 2022, 85 (2), pp.16. ⟨10.1007/s00285-022-01784-6⟩. ⟨hal-03618303v2⟩

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