Stability and Asymptotic Behaviour for the Numerical Solution of a Reaction—Diffusion Model for a Deterministic Diffusive Epidemic

1983 ◽  
Vol 3 (3) ◽  
pp. 341-351
Author(s):  
LUCIANO LOPEZ
Keyword(s):  
Asymptotic Behaviour ◽  
Numerical Solution ◽  
Diffusion Model ◽  
Reaction Diffusion ◽  
Reaction Diffusion Model

scholarly journals Validation of numerical solution of diffusive part in a reaction–diffusion model

2017 ◽  
Vol 74 (1) ◽  
pp. 143-156 ◽  
Author(s):  
E.C. Herrera-Hernández ◽  
M. Núñez-López ◽  
J.A. González-Calderón
Keyword(s):  
Numerical Solution ◽  
Diffusion Model ◽  
Reaction Diffusion ◽  
Reaction Diffusion Model ◽  
Diffusive Part

Asymptotic behaviour, uniqueness and stability of coexistence states of a non-cooperative reaction–diffusion model of nuclear reactors

2010 ◽  
Vol 140 (1) ◽  
pp. 189-201 ◽  
Author(s):  
Rui Peng ◽  
Dong Wei ◽  
Guoying Yang
Keyword(s):  
Asymptotic Behaviour ◽  
Diffusion Model ◽  
Blow Up ◽  
Nuclear Reactors ◽  
Reaction Diffusion ◽  
Fast Neutrons ◽  
Fuel Temperature ◽  
Reaction Diffusion Model ◽  
Coexistence States ◽  
Spatial Dimensions

We investigate a non-cooperative reaction-diffusion model arising in the theory of nuclear reactors and are concerned with the associated steady-state problem. We determine the asymptotic behaviour of the coexistence states near the point of bifurcation from infinity, which exhibits the following very interesting spatial blow-up pattern: when the fuel temperature reaches a certain value, the free fast neutrons undergoing nuclear reaction will blow up in each spatial point of the interior of the reactor. Without any restriction on spatial dimensions, we also discuss the uniqueness and stability of the coexistence states. Our results complement and sharpen those derived in two recent works by Arioli and Lóopez-Gómez.

scholarly journals Numerical solution of a coupled reaction-diffusion model using barycentric interpolation collocation method

2020 ◽  
Vol 24 (4) ◽  
pp. 2561-2567
Author(s):  
Yu Zhang ◽  
Wei Zhang ◽  
Chenhui Zhao ◽  
Yulan Wang
Keyword(s):  
Approximate Solution ◽  
Numerical Solution ◽  
Collocation Method ◽  
Diffusion Model ◽  
Numerical Experiments ◽  
Reaction Diffusion ◽  
Barycentric Interpolation ◽  
Reaction Diffusion Model ◽  
Linear Reaction ◽  
Coupled Reaction

In thermal science, chemical and mechanics, the non-linear reaction-diffusion model is very important, and an approximate solution with high precision is always needed. In this article, the barycentric interpolation collocation method is proposed for this purpose. Numerical experiments show that the proposed approach is highly reliable.

Asymptotic behaviour of a reaction–diffusion model with a quiescent stage

2007 ◽  
Vol 463 (2080) ◽  
pp. 1029-1043 ◽  
Author(s):  
Kate Fang Zhang ◽  
Xiao-Qiang Zhao
Keyword(s):  
Asymptotic Behaviour ◽  
Diffusion Model ◽  
Wave Speed ◽  
Global Attractivity ◽  
Travelling Waves ◽  
Reaction Diffusion ◽  
Reaction Diffusion Model ◽  
Asymptotic Speed ◽  
Minimal Wave Speed ◽  
Quiescent Stage

This paper is devoted to the investigation of the asymptotic behaviour for a reaction–diffusion model with a quiescent stage. We first establish the existence of the asymptotic speed of spread and show that it coincides with the minimal wave speed for monotone travelling waves. Then we obtain a threshold result on the global attractivity of either zero or positive steady state in the case where the spatial domain is bounded.

scholarly journals A new analyzing technique for nonlinear time fractional Cauchy reaction-diffusion model equations

2020 ◽  
Vol 19 ◽  
pp. 103462 ◽  
Author(s):  
Hijaz Ahmad ◽  
Tufail A. Khan ◽  
Imtiaz Ahmad ◽  
Predrag S. Stanimirović ◽  
Yu-Ming Chu
Keyword(s):  
Diffusion Model ◽  
Reaction Diffusion ◽  
Reaction Diffusion Model ◽  
Model Equations
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