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On simulation of reaction-diffusion systems containing self and cross-diffusion

Benjamin Aymard 1
1 MATHNEURO - Mathématiques pour les Neurosciences
CRISAM - Inria Sophia Antipolis - Méditerranée
Abstract : In this article we study reaction-diffusion systems containing self and cross-diffusion using a free energy approach. This framework naturally leads to the formulation of an energy law, and to a numerical method respecting a discrete version of the latter (a linear second order finite-element method with adaptive mesh refinement). Applying this numerical scheme to a Gray-Scott system augmented with self and cross-diffusion terms, we verify numerically the energy law, and unveil patterns distinct from those obtained with linear diffusion.
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Preprints, Working Papers, ...
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https://hal.inria.fr/hal-02460169
Contributor : Benjamin Aymard <>
Submitted on : Wednesday, January 29, 2020 - 8:40:25 PM
Last modification on : Friday, January 31, 2020 - 4:12:28 PM

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  • HAL Id : hal-02460169, version 1
  • ARXIV : 2001.10069

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Benjamin Aymard. On simulation of reaction-diffusion systems containing self and cross-diffusion. 2020. ⟨hal-02460169⟩

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