Stability Analysis of Reaction-Diffusion Equations with Double Diffusivity System

Ahmed Kasem,Saad Manna

doi:10.33899/csmj.2010.163882

Abstract

12 2 1 12 D k aL k bL k ba L ba L0 '' ' ' '' +++-> ABSTRACT Stability analysis for steady state solution of reaction-diff usion equations with double diffusivity discuss and arise in the solution of problems of flow of homogeneous liquids and heat conduction involving air-temperature ) , ( t x u and a grain-temperat ure

Highlights

Reaction-diffusion give rise to texture synthesis based on the simulation of a process of local nonlinear interactions, which has been proposed as a model of biological pattern formation
A chemical mechanism that was first proposed by Alan [10] (1952) to account for pattern formation in biological morphogenesis, he postulated that patterning is governed primarily by concurrently operating processes: diffusion of morphogens through the tissue and chemical reactions that produce and destroy morphogens at a rate that depends, among other things, on their concentrations
Aggarwala and Nasim [2] derived the solution of reaction-diffusion equations with double diffusivity by laplace technique and fourier transforms which appear to be simpler and more direct

Summary

Introduction

Reaction-diffusion give rise to texture synthesis based on the simulation of a process of local nonlinear interactions, which has been proposed as a model of biological pattern formation. A chemical mechanism that was first proposed by Alan [10] (1952) to account for pattern formation in biological morphogenesis, he postulated that patterning is governed primarily by concurrently operating processes: diffusion of morphogens through the tissue and chemical reactions that produce and destroy morphogens at a rate that depends, among other things, on their concentrations. Such mechanisms are called reaction-diffusion (RD) systems [11]. We will study the stability analysis of steady state solution of double diffusivity model

Model of equations

Stability analysis

Solution of the steady state case