scholarly journals Large-time behavior of a two-scale semilinear reaction-diffusion system for concrete sulfatation

2014 ◽  
Vol 38 (7) ◽  
pp. 1451-1464
Author(s):  
Toyohiko Aiki ◽  
Adrian Muntean
Keyword(s):  
Large Time ◽  
Reaction Diffusion ◽  
Large Time Behavior ◽  
Reaction Diffusion System ◽  
Diffusion System ◽  
Time Behavior

Global existence and large time behavior of solutions of a time fractional reaction diffusion system

2020 ◽  
Vol 23 (2) ◽  
pp. 390-407
Author(s):  
Ahmed Alsaedi ◽  
Bashir Ahmad ◽  
Mokhtar Kirane ◽  
Rafika Lassoued
Keyword(s):  
Global Existence ◽  
Large Time ◽  
Reaction Diffusion ◽  
Large Time Behavior ◽  
Positive Answer ◽  
Reaction Diffusion System ◽  
Diffusion System ◽  
Time Behavior ◽  
Feedback Method ◽  
Fractional Reaction

AbstractIn this paper, it is proved that a time fractional reaction diffusion system with reaction terms of the Brusselator type admits a global solution by using the feedback method of F. Rothe [20]. Furthermore, some results on the large time behavior of the solutions are obtained. We give a positive answer to Problem 6 of the valuable paper of Gal and Warma [6].

ASYMPTOTIC EQUIVALENCE OF A REACTION-DIFFUSION SYSTEM TO THE CORRESPONDING SYSTEM OF ORDINARY DIFFERENTIAL EQUATIONS

1995 ◽  
Vol 05 (06) ◽  
pp. 813-834 ◽  
Author(s):  
HIROKI HOSHINO ◽  
SHUICHI KAWASHIMA
Keyword(s):  
Differential Equations ◽  
Ordinary Differential Equations ◽  
Energy Method ◽  
Large Time ◽  
Reaction Diffusion ◽  
Large Time Behavior ◽  
Reaction Diffusion System ◽  
Diffusion System ◽  
Time Behavior ◽  
Asymptotic Equivalence

Large time behavior of the solution to some simple reaction-diffusion system is studied. It is proved that the solution behaves like the solution to the corresponding system of ordinary differential equations as time goes to infinity. The proof is based on an energy method combined with the Lp−Lqestimate for the associated semigroup.

scholarly journals Boundedness and Large-Time Behavior Results for a Diffusive Epidemic Model

2007 ◽  
Vol 2007 ◽  
pp. 1-15 ◽  
Author(s):  
Lamine Melkemi ◽  
Ahmed Zerrouk Mokrane ◽  
Amar Youkana
Keyword(s):  
Asymptotic Behavior ◽  
Large Time ◽  
System Modeling ◽  
Uniform Boundedness ◽  
Reaction Diffusion ◽  
Large Time Behavior ◽  
Positive Answer ◽  
Time Behavior ◽  
Epidemic Disease ◽  
Infection Disease

We consider a reaction-diffusion system modeling the spread of an epidemic disease within a population divided into the susceptible and infective classes. We first consider the question of the uniform boundedness of the solutions for which we give a positive answer. Then we deal with the asymptotic behavior of the solutions where in particular we are interested in reasonable conditions leading to the extinction of the infection disease as the time goes to infinity.

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