Turing-type instabilities in bulk–surface reaction–diffusion systems

Andreas Rätz ^[1]
1. [1] Technical University of Dortmund
  
  Technical University of Dortmund
  
  Kreisfreie Stadt Dortmund, Alemania
Localización: Journal of computational and applied mathematics, ISSN 0377-0427, Vol. 289, Nº 1 (1 December 2015), 2015, págs. 142-152
Idioma: inglés
DOI: 10.1016/j.cam.2015.02.050
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Resumen
- In this contribution we consider a coupled bulk–surface reaction–diffusion system and for infinitely fast bulk diffusion its formal reduction to a non-local surface PDE model. Thereby, we review results of linear stability analyses for both models showing that Turing-type instabilities can occur for equal lateral diffusion coefficients. The stability results are confirmed by new numerical results. As a specific application, we study a model for a spatial and reaction cycle of signalling molecules in a cell.