scholarly journals Exponential decay towards equilibrium and global classical solutions for nonlinear reaction–diffusion systems

2016 ◽  
Vol 16 (3) ◽  
pp. 681-704 ◽  
Author(s):  
Klemens Fellner ◽  
El-Haj Laamri
Keyword(s):  
Exponential Decay ◽  
Reaction Diffusion ◽  
Classical Solutions ◽  
Reaction Diffusion Systems ◽  
Global Classical Solutions ◽  
Nonlinear Reaction ◽  
Diffusion Systems

scholarly journals CAS WAVELETS METHOD TO SOLVE REACTION-DIFFUSION SYSTEM AND COMPARE IT WITH (G.F.E) METHOD

2020 ◽  
Vol 17 (35) ◽  
pp. 1110-1123
Author(s):  
Badran Jasim SALIM ◽  
Oday Ahmed JASIM
Keyword(s):  
Steady State ◽  
Finite Elements ◽  
Reaction Diffusion ◽  
Partial Differential ◽  
Reaction Diffusion Systems ◽  
Time Frequency ◽  
Nonlinear Reaction ◽  
Diffusion Systems ◽  
Cas Wavelets ◽  
Steady State Solutions

Wavelet analysis plays a prominent role in various fields of scientific disciplines. Mainly, wavelets are very successfully used in signal analysis for waveform representation and segmentation, time-frequency analysis, and fast algorithms in the propagation equations and reaction. This research aimed to guide researchers to use Cos and Sin (CAS) to approximate the solution of the partial differential equation system. This method has been successfully applied to solve a coupled system of nonlinear Reaction-diffusion systems. It has been shown CAS wavelet method is quite capable and suited for finding exact solutions once the consistency of the method gives wider applicability where the main idea is to transform complex nonlinear partial differential equations into algebraic equation systems, which are easy to handle and find a numerical solution for them. By comparing the numerical solutions of the CAS and Galerkin finite elements methods, the answer of nonlinear Reaction-diffusion systems using the CAS wavelets for all tˆ and x values is accurate, reliable, robust, promising, and quickly arrives at the exact solution. When parameters 𝜀1 𝑎𝑛𝑑 𝜀2 are growing and with L decreasing, then the CAS method converges to steady-state solutions quickly (the less L, the more accurate the solution). It is converging towards steady-state solutions faster than and loses steps over time. Moreover, the results also show that the solution of the CAS wavelets is more reliable and faster compared to the Galerkin finite elements (G.F.E).

Nonlinear reaction diffusion systems of degenerate parabolic type

2009 ◽  
pp. 373-400
Author(s):  
Tarik Aliziane ◽  
Lila Hadjadj ◽  
Mohamed Said Moulay
Keyword(s):  
Parabolic Type ◽  
Reaction Diffusion ◽  
Reaction Diffusion Systems ◽  
Nonlinear Reaction ◽  
Diffusion Systems ◽  
Degenerate Parabolic
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