Nonlinear Diffusion–Reaction Phenomena

2012 ◽  
pp. 381-423
Author(s):  
Lokenath Debnath
Keyword(s):  
Nonlinear Diffusion ◽  
Diffusion Reaction

Solitary and Travelling Wave Solutions of Certain Nonlinear Diffusion-Reaction Equations

2020 ◽  
Author(s):  
Miftachul Hadi
Keyword(s):  
Nonlinear Diffusion ◽  
Travelling Wave ◽  
Diffusion Reaction ◽  
Travelling Wave Solutions ◽  
Wave Solutions ◽  
Reaction Equations

We review the work of Ranjit Kumar, R S Kaushal, Awadhesh Prasad. The work is still in progress.

A dynamical study of certain nonlinear diffusion–reaction equations with a nonlinear convective flux term

Pramana ◽  
2018 ◽  
Vol 92 (1) ◽  
Author(s):  
Anand Malik ◽  
Hitender Kumar ◽  
Rishi Pal Chahal ◽  
Fakir Chand
Keyword(s):  
Nonlinear Diffusion ◽  
Diffusion Reaction ◽  
Dynamical Study ◽  
Convective Flux ◽  
Reaction Equations

scholarly journals A structural approach to control of transitional waves of nonlinear diffusion-reaction systems: Theory and possible applications to bio-medicine

2002 ◽  
Vol 7 (1) ◽  
pp. 27-40 ◽  
Author(s):  
Victor Kardashov ◽  
Shmuel Einav
Keyword(s):  
Nonlinear Diffusion ◽  
Structural Parameters ◽  
Deterministic Chaos ◽  
Reaction Diffusion ◽  
Diffusion Reaction ◽  
Reaction Diffusion Systems ◽  
Diffusion Systems ◽  
Novel Approach ◽  
Dynamics Models ◽  
And Control

This paper has considered a novel approach to structural recognition and control of nonlinear reaction-diffusion systems (systems with density dependent diffusion). The main consistence of the approach is interactive variation of the nonlinear diffusion and sources structural parameters that allows to implement a qualitative control and recognition of transitional system conditions (transients). The method of inverse solutions construction allows formulating the new analytic conditions of compactness and periodicity of the transients that is also available for nonintegrated systems. On the other hand, using of energy conservations laws, allows transfer to nonlinear dynamics models that gives the possiblity to apply the modern deterministic chaos theory (particularly the Feigenboum's universal constants and scenario of chaotic transitions).

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