Stability of patterns and of constant steady states for a cross-diffusion system

G. Svantnerné Sebestyén ^[1] ; István Faragó ^[1] ; Róbert Horváth ^[2] ; R. Kersner ^[3] ; M. Klincsik ^[3]
1. [1] Eötvös Loránd University
  
  Eötvös Loránd University
  
  Hungría
2. [2] Budapest University of Technology and Economics
  
  Budapest University of Technology and Economics
  
  Hungría
3. [3] University of Pecs
  
  University of Pecs
  
  Hungría
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Localización: Journal of computational and applied mathematics, ISSN 0377-0427, Vol. 293, Nº 1 (February 2016), 2016, págs. 208-216
Idioma: inglés
DOI: 10.1016/j.cam.2015.03.041
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Resumen
- This paper considers mathematical and numerical models of normal and abnormal tissue growth. To this aim, we analyse a nonlinear system of partial differential equations, called as cross-diffusion system, in a rather general form. We investigate the dynamics of the system in dependence on the system parameters. We show analytically the existence of a periodic stationary solution for the set of certain positive initial data. The other choices of the parameters are investigated by construction of corresponding numerical models. We also analyse the stability of the stationary solutions. Numerical examples demonstrate our results.