Traveling wavefronts of a nonlinear reaction–diffusion model of tumor growth under the acid environment

2014 ◽  
Vol 07 (03) ◽  
pp. 1450034
Author(s):  
Huiyan Zhu ◽  
Yang Luo ◽  
Xiufang Wang
Keyword(s):  
Diffusion Model ◽  
Perturbation Methods ◽  
Tumor Tissue ◽  
Reaction Diffusion ◽  
Traveling Wave Solution ◽  
Ion Concentration ◽  
Banach Fixed Point Theorem ◽  
Nonlinear Reaction ◽  
Reaction Diffusion Model ◽  
Acid Environment

In this paper, a reaction–diffusion model describing temporal development of tumor tissue, normal tissue and excess H+ ion concentration is considered. Based on a combination of perturbation methods, the Fredholm theory and Banach fixed point theorem, we theoretically justify the existence of the traveling wave solution for this model.

scholarly journals A solvable nonlinear reaction-diffusion model

1995 ◽  
Vol 198 (2) ◽  
pp. 100-104 ◽  
Author(s):  
Max-Olivier Hongler ◽  
Ricardo Lima
Keyword(s):  
Diffusion Model ◽  
Reaction Diffusion ◽  
Nonlinear Reaction ◽  
Reaction Diffusion Model

scholarly journals New Exact Solutions of the Brusselator Reaction Diffusion Model Using the Exp-Function Method

2009 ◽  
Vol 2009 ◽  
pp. 1-9 ◽  
Author(s):  
F. Khani ◽  
F. Samadi ◽  
S. Hamedi-Nezhad
Keyword(s):  
Exact Solutions ◽  
Diffusion Model ◽  
Function Method ◽  
Soliton Solutions ◽  
Reaction Diffusion ◽  
Reaction Diffusion Equation ◽  
New Exact Solutions ◽  
Nonlinear Reaction ◽  
Nonlinear Reaction Diffusion Equation ◽  
Reaction Diffusion Model

Firstly, using a series of transformations, the Brusselator reaction diffusion model is reduced into a nonlinear reaction diffusion equation, and then through using Exp-function method, more new exact solutions are found which contain soliton solutions. The suggested algorithm is quite efficient and is practically well suited for use in these problems. The results show the reliability and efficiency of the proposed method.

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