Dissipative structures in a nonlinear reaction-diffusion model with forward inhibition. stability of secondary multiple steady states

1979 ◽  
Vol 16 (3) ◽  
pp. 421-432 ◽  
Author(s):  
V. Fairén ◽  
M.G. Velarde
Keyword(s):  
Diffusion Model ◽  
Reaction Diffusion ◽  
Dissipative Structures ◽  
Steady States ◽  
Multiple Steady States ◽  
Nonlinear Reaction ◽  
Reaction Diffusion Model

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 Multiple stable steady states of a reaction-diffusion model on zebrafish dorsal-ventral patterning

2011 ◽  
Vol 4 (6) ◽  
pp. 1413-1428 ◽  
Author(s):  
Wenrui Hao ◽  
◽  
Jonathan D. Hauenstein ◽  
Bei Hu ◽  
Yuan Liu ◽  
...  
Keyword(s):  
Diffusion Model ◽  
Reaction Diffusion ◽  
Steady States ◽  
Reaction Diffusion 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
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