A weak solution approach to a reaction-diffusion system modeling pattern formation on seashells

2009 ◽  
Vol 32 (17) ◽  
pp. 2267-2286 ◽  
Author(s):  
Jan Kelkel ◽  
Christina Surulescu
Keyword(s):  
Weak Solution ◽  
Pattern Formation ◽  
System Modeling ◽  
Reaction Diffusion ◽  
Reaction Diffusion System ◽  
Diffusion System ◽  
Solution Approach

A NUMERICAL ANALYSIS OF A REACTION–DIFFUSION SYSTEM MODELING THE DYNAMICS OF GROWTH TUMORS

2010 ◽  
Vol 20 (05) ◽  
pp. 731-756 ◽  
Author(s):  
VERÓNICA ANAYA ◽  
MOSTAFA BENDAHMANE ◽  
MAURICIO SEPÚLVEDA
Keyword(s):  
Weak Solution ◽  
Numerical Analysis ◽  
Numerical Scheme ◽  
System Modeling ◽  
Reaction Diffusion ◽  
Reaction Diffusion System ◽  
Diffusion System ◽  
Existence Of Weak Solutions ◽  
Early Tumor ◽  
Volume Method

We consider a reaction–diffusion system of 2 × 2 equations modeling the spread of early tumor cells. The existence of weak solutions is ensured by a classical argument of Faedo–Galerkin method. Then, we present a numerical scheme for this model based on a finite volume method. We establish the existence of discrete solutions to this scheme, and we show that it converges to a weak solution. Finally, some numerical simulations are reported with pattern formation examples.

Programmable reactions and diffusion using DNA for pattern formation in hydrogel medium

2019 ◽  
Vol 4 (3) ◽  
pp. 639-643 ◽  
Author(s):  
Keita Abe ◽  
Ibuki Kawamata ◽  
Shin-ichiro M. Nomura ◽  
Satoshi Murata
Keyword(s):  
Pattern Formation ◽  
Reaction Diffusion ◽  
Reaction Diffusion System ◽  
Diffusion System ◽  
And Diffusion

We demonstrate a method of pattern formation based on an artificial reaction diffusion system in hydrogel medium.

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