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Improved duality estimates: time discrete case and applications to a class of cross-diffusion systems

Thomas Lepoutre 1, 2, 3
1 DRACULA - Multi-scale modelling of cell dynamics : application to hematopoiesis
ICJ - Institut Camille Jordan [Villeurbanne], Inria Grenoble - Rhône-Alpes, CGPhiMC - Centre de génétique et de physiologie moléculaire et cellulaire
3 MMCS - Modélisation mathématique, calcul scientifique
ICJ - Institut Camille Jordan [Villeurbanne]
Abstract : We adapt the improved duality estimates for bounded coefficients derived by Canizo et al. to the framework of cross diffusion. Since the estimates can not be directly applied we need to derive a time discrete version of their results and apply it to an implicit semi-discretization in time of the cross diffusion systems. This leads to new global existence results for cross diffusion systems with bounded cross diffusion pressures and potentially superquadratic reaction.
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https://hal.inria.fr/hal-01943576
Contributor : Thomas Lepoutre <>
Submitted on : Monday, December 3, 2018 - 10:42:08 PM
Last modification on : Wednesday, July 8, 2020 - 12:43:59 PM
Long-term archiving on: : Monday, March 4, 2019 - 3:31:03 PM

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  • HAL Id : hal-01943576, version 1
  • ARXIV : 1812.01296

Citation

Thomas Lepoutre. Improved duality estimates: time discrete case and applications to a class of cross-diffusion systems. Communications in Mathematical Sciences, International Press, 2019, 17 (2), pp.1-17. ⟨hal-01943576⟩

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