Global Existence, Asymptotic Stability and Numerical Simulation for Reaction-Diffusion Systems with Exponential Nonlinearity on Growing Domains

2021 ◽  
Author(s):  
Redouane Douaifia ◽  
Salem Abdelmalek ◽  
Belgacem Rebiai
Keyword(s):  
Numerical Simulation ◽  
Asymptotic Stability ◽  
Global Existence ◽  
Reaction Diffusion ◽  
Exponential Nonlinearity ◽  
Reaction Diffusion Systems ◽  
Diffusion Systems

Global Existence for Quadratic Systems of Reaction-Diffusion

2007 ◽  
Vol 7 (3) ◽  
Author(s):  
Laurent Desvillettes ◽  
Klemens Fellner ◽  
Michel Pierre ◽  
Julien Vovelle
Keyword(s):  
Global Existence ◽  
Weak Solutions ◽  
A Priori ◽  
Reaction Diffusion ◽  
Quadratic Systems ◽  
Reaction Diffusion Systems ◽  
Diffusion Systems ◽  
L Log L

AbstractWe prove global existence in time of weak solutions to a class of quadratic reaction-diffusion systems for which a Lyapounov structure of L log L-entropy type holds. The approach relies on an a priori dimension-independent L

scholarly journals An Algebraic Method on the Eigenvalues and Stability of Delayed Reaction-Diffusion Systems

2013 ◽  
Vol 2013 ◽  
pp. 1-7
Author(s):  
Jian Ma ◽  
Baodong Zheng
Keyword(s):  
Asymptotic Stability ◽  
Linear Operator ◽  
Reaction Diffusion ◽  
Matrix Pencil ◽  
Algebraic Method ◽  
Delayed Reaction ◽  
Reaction Diffusion Systems ◽  
Diffusion Systems ◽  
The Matrix ◽  
Pure Imaginary Eigenvalues

The eigenvalues and stability of the delayed reaction-diffusion systems are considered using the algebraic methods. Firstly, new algebraic criteria to determine the pure imaginary eigenvalues are derived by applying the matrix pencil and the linear operator methods. Secondly, a practical checkable criteria for the asymptotic stability are introduced.

Global Existence for Reaction-Diffusion Systems Modelling Ignition

1998 ◽  
Vol 142 (3) ◽  
pp. 219-251 ◽  
Author(s):  
Miguel A. Herrero ◽  
Andrew A. Lacey ◽  
Juan J. L. Velázquez
Keyword(s):  
Global Existence ◽  
Reaction Diffusion ◽  
Reaction Diffusion Systems ◽  
Diffusion Systems ◽  
Systems Modelling

scholarly journals The amplitude system for a Simultaneous short-wave Turing and long-wave Hopf instability

2021 ◽  
Vol 0 (0) ◽  
pp. 0
Author(s):  
Guido Schneider ◽  
Matthias Winter
Keyword(s):  
Numerical Simulation ◽  
Analytical Approach ◽  
Reaction Diffusion ◽  
Short Wave ◽  
Reaction Diffusion Systems ◽  
Long Wave ◽  
Diffusion Systems ◽  
Schnakenberg Model ◽  
Pattern Forming ◽  
Amplitude System

<p style='text-indent:20px;'>We consider reaction-diffusion systems for which the trivial solution simultaneously becomes unstable via a short-wave Turing and a long-wave Hopf instability. The Brusseletor, Gierer-Meinhardt system and Schnakenberg model are prototype biological pattern forming systems which show this kind of behavior for certain parameter regimes. In this paper we prove the validity of the amplitude system associated to this kind of instability. Our analytical approach is based on the use of mode filters and normal form transformations. The amplitude system allows us an efficient numerical simulation of the original multiple scaling problems close to the instability.</p>

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