scholarly journals Variational principle for the asymptotic speed of fronts of the density-dependent diffusion-reaction equation

1995 ◽  
Vol 52 (3) ◽  
pp. 3285-3287 ◽  
Author(s):  
R. D. Benguria ◽  
M. C. Depassier
Keyword(s):  
Variational Principle ◽  
Diffusion Reaction ◽  
Reaction Equation ◽  
Density Dependent ◽  
Asymptotic Speed

scholarly journals Multiplier method and exact solutions for a density dependent reaction-diffusion equation

2016 ◽  
Vol 1 (2) ◽  
pp. 311-320 ◽  
Author(s):  
M. Rosa ◽  
M. L Gandarias
Keyword(s):  
Conservation Laws ◽  
Direct Method ◽  
Reaction Diffusion ◽  
Reaction Diffusion Equations ◽  
Reaction Diffusion Equation ◽  
Diffusion Reaction ◽  
Reaction Equation ◽  
Density Dependent ◽  
Population Dynamics Models ◽  
Dynamics Models

AbstractReaction-diffusion equations have enjoyed a considerable amount of scientific interest. The reason for the large amount of work put into studying these equations is not only their practical relevance, but also interesting phenomena that can arise from such equations. Fisher equation is commonly used in biology for population dynamics models and in bacterial growth problems as well as development and growth of solid tumours. The physical aspects of this equation are not fully understood without getting deeper into the concept of conservation laws. In [4], Anco and Bluman gave a general treatment of a direct conservation law method for partial differential equations expressed in a standard Cauchy-Kovaleskaya form. In this work we study the well known density dependent diffusion-reaction equation. We derive conservation laws by using the direct method of the multipliers.

Simulations on Expansive Strain of Concrete Caused by Ettringite Growth under Sulfate Attack

2011 ◽  
Vol 250-253 ◽  
pp. 1906-1911 ◽  
Author(s):  
Xiao Bao Zuo ◽  
Wei Sun
Keyword(s):  
Sulfate Solution ◽  
Sulfate Attack ◽  
Diffusion Time ◽  
Diffusion Reaction ◽  
Sulfate Ion ◽  
Reaction Equation ◽  
Ettringite Formation ◽  
Sulfate Solutions ◽  
Calcium Aluminates ◽  
Strain Responses

In order to assess theoretically the expansive strain of concrete caused by the ettringite formation and growth under the sulfate attack, some models are proposed to investigate the strain responses of concrete exposed to the sulfate solutions. Firstly, an 1-D nonlinear and nonsteady diffusion-reaction equation of sulfate ion in concrete is proposed; Secondly, based on chemical reactions between sulfate and aluminates in concrete, the expansive strain is obtained due to the ettringite growth resulting in concrete expansion. Thirdly, numerical simulations are carried out to analyze the formation process of the concrete expansive strain under the sulfate solution, and results show that the models can be used to predict the concrete responses with the diffusion time, such as the distribution concentration of sulfate ion, dissipated concentration of the calcium aluminates, expansion strain of concrete due to the formation and growth of ettringite.

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