Global weak solution for a singular two-component reaction-diffusion system

2013 ◽  
Vol 46 (1) ◽  
pp. 1-13 ◽  
Author(s):  
Arnaud Ducrot ◽  
Michel Langlais
Keyword(s):  
Weak Solution ◽  
Reaction Diffusion ◽  
Global Weak Solution ◽  
Reaction Diffusion System ◽  
Diffusion System ◽  
Two Component

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.

scholarly journals Pattern formation in a two-component reaction–diffusion system with delayed processes on a network

2016 ◽  
Vol 462 ◽  
pp. 230-249 ◽  
Author(s):  
Julien Petit ◽  
Malbor Asllani ◽  
Duccio Fanelli ◽  
Ben Lauwens ◽  
Timoteo Carletti
Keyword(s):  
Pattern Formation ◽  
Reaction Diffusion ◽  
Reaction Diffusion System ◽  
Diffusion System ◽  
Two Component

scholarly journals Numerical Simulation and Symmetry Reduction of a Two-Component Reaction-Diffusion System

2020 ◽  
Vol 2020 ◽  
pp. 1-5
Author(s):  
Jina Li ◽  
Xuehui Ji
Keyword(s):  
Numerical Simulation ◽  
Differential Equations ◽  
Ordinary Differential Equations ◽  
Reaction Diffusion ◽  
Symmetry Reduction ◽  
Reaction Diffusion System ◽  
Diffusion System ◽  
Symmetry Classification ◽  
Two Component

In this paper, the symmetry classification and symmetry reduction of a two-component reaction-diffusion system are investigated, the reaction-diffusion system can be reduced to system of ordinary differential equations, and the solutions and numerical simulation will be showed by examples.

scholarly journals Motion of a Spot in a Reaction Diffusion System under the Influence of Chemotaxis

2018 ◽  
Vol 2018 ◽  
pp. 1-24
Author(s):  
Satoshi Kawaguchi
Keyword(s):  
Reaction Diffusion ◽  
Equation Of Motion ◽  
Circular Motion ◽  
Reaction Diffusion System ◽  
Diffusion System ◽  
Coupling Term ◽  
Two Component ◽  
Global Coupling ◽  
Time Evolution Equation ◽  
Critical Intensity

We consider the motion of a spot under the influence of chemotaxis. We propose a two-component reaction diffusion system with a global coupling term and a Keller-Segel type chemotaxis term. For the system, we derive the equation of motion of the spot and the time evolution equation of the tensors. We show the existence of an upper limit for the velocity and a critical intensity for the chemotaxis, over which there is no circular motion. The chemotaxis suppresses the range of velocity for the circular motion. This braking effect on velocity originates from the refractory period behind the rear interface of the spot and the negative chemotactic velocity. The physical interpretation of the results and its plausibility are discussed.

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