Novel decay laws for the one-dimensional reaction - diffusion model as consequence of initial distributions

1997 ◽  
Vol 30 (10) ◽  
pp. 3299-3311 ◽  
Author(s):  
Pablo A Alemany
Keyword(s):  
Diffusion Model ◽  
Reaction Diffusion ◽  
One Dimensional ◽  
Reaction Diffusion Model ◽  
The One ◽  
Initial Distributions

Pyrolysis behaviors dominated by the reaction–diffusion mechanism in the fluorine-free metal–organic decomposition process

2020 ◽  
Vol 8 (48) ◽  
pp. 17417-17428
Author(s):  
Jiangtao Shi ◽  
Yue Zhao ◽  
Yue Wu ◽  
Jingyuan Chu ◽  
Xiao Tang ◽  
...  
Keyword(s):  
Diffusion Model ◽  
Diffusion Mechanism ◽  
Reaction Diffusion ◽  
Decomposition Process ◽  
One Dimensional ◽  
Reaction Diffusion Model ◽  
Metal Organic ◽  
Free Metal ◽  
Organic Decomposition

In this work, pyrolysis behaviors dominated by the reaction–diffusion mechanism were investigated. And one-dimensional reaction–diffusion model is proposed.

scholarly journals Distributed Parameter State Estimation for the Gray–Scott Reaction-Diffusion Model

Systems ◽  
2021 ◽  
Vol 9 (4) ◽  
pp. 71
Author(s):  
Petro Feketa ◽  
Alexander Schaum ◽  
Thomas Meurer
Keyword(s):  
Finite Number ◽  
Exponential Convergence ◽  
Reaction Diffusion ◽  
Distributed Parameter ◽  
System State ◽  
State Information ◽  
One Dimensional ◽  
Reaction Diffusion Model ◽  
Complete State ◽  
The One

A constructive approach is provided for the reconstruction of stationary and non-stationary patterns in the one-dimensional Gray-Scott model, utilizing measurements of the system state at a finite number of locations. Relations between the parameters of the model and the density of the sensor locations are derived that ensure the exponential convergence of the estimated state to the original one. The designed observer is capable of tracking a variety of complex spatiotemporal behaviors and self-replicating patterns. The theoretical findings are illustrated in particular numerical case studies. The results of the paper can be used for the synchronization analysis of the master–slave configuration of two identical Gray–Scott models coupled via a finite number of spatial points and can also be exploited for the purposes of feedback control applications in which the complete state information is required.

On a reaction–diffusion model for sterile insect release method on a bounded domain

2014 ◽  
Vol 07 (03) ◽  
pp. 1450030 ◽  
Author(s):  
Weihua Jiang ◽  
Xin Li ◽  
Xingfu Zou
Keyword(s):  
Sufficient Conditions ◽  
Reaction Diffusion ◽  
One Dimensional ◽  
Reaction Diffusion Model ◽  
Whole Space ◽  
The One ◽  
Sterile Insect Release ◽  
Release Method ◽  
Dimensional Domain ◽  
Sterile Insect Release Method

We consider a system of partial differential equations that describes the interaction of the sterile and fertile species undergoing the sterile insect release method (SIRM). Unlike in the previous work [M. A. Lewis and P. van den Driessche, Waves of extinction from sterile insect release, Math. Biosci.5 (1992) 221–247] where the habitat is assumed to be the one-dimensional whole space ℝ, we consider this system in a bounded one-dimensional domain (interval). Our goal is to derive sufficient conditions for success of the SIRM. We show the existence of the fertile-free steady state and prove its stability. Using the releasing rate as the parameter, and by a saddle-node bifurcation analysis, we obtain conditions for existence of two co-persistence steady states, one stable and the other unstable. Biological implications of our mathematical results are that: (i) when the fertile population is at low level, the SIRM, even with small releasing rate, can successfully eradicate the fertile insects; (ii) when the fertile population is at a higher level, the SIRM can succeed as long as the strength of the sterile releasing is large enough, while the method may also fail if the releasing is not sufficient.

Stability and Hopf Bifurcation in a Reaction–Diffusion Model with Chemotaxis and Nonlocal Delay Effect

2018 ◽  
Vol 28 (04) ◽  
pp. 1850046 ◽  
Author(s):  
Dong Li ◽  
Shangjiang Guo
Keyword(s):  
Hopf Bifurcation ◽  
Diffusion Model ◽  
Dirichlet Boundary ◽  
Reaction Diffusion ◽  
High Concentration ◽  
Delay Effect ◽  
One Dimensional ◽  
Nonlocal Delay ◽  
Reaction Diffusion Model ◽  
Steady State Solutions

Chemotaxis is an observed phenomenon in which a biological individual moves preferentially toward a relatively high concentration, which is contrary to the process of natural diffusion. In this paper, we study a reaction–diffusion model with chemotaxis and nonlocal delay effect under Dirichlet boundary condition by using Lyapunov–Schmidt reduction and the implicit function theorem. The existence, multiplicity, stability and Hopf bifurcation of spatially nonhomogeneous steady state solutions are investigated. Moreover, our results are illustrated by an application to the model with a logistic source, homogeneous kernel and one-dimensional spatial domain.

Stabilization of Dominant Structures in an Ionic Reaction-Diffusion System

1998 ◽  
Vol 63 (6) ◽  
pp. 761-769 ◽  
Author(s):  
Roland Krämer ◽  
Arno F. Münster
Keyword(s):  
Reaction Diffusion ◽  
Dominant Mode ◽  
Reaction Diffusion System ◽  
Diffusion System ◽  
Local Perturbation ◽  
Dimensional System ◽  
One Dimensional ◽  
Brusselator Model ◽  
The One ◽  
Dominant Structure

We describe a method of stabilizing the dominant structure in a chaotic reaction-diffusion system, where the underlying nonlinear dynamics needs not to be known. The dominant mode is identified by the Karhunen-Loeve decomposition, also known as orthogonal decomposition. Using a ionic version of the Brusselator model in a spatially one-dimensional system, our control strategy is based on perturbations derived from the amplitude function of the dominant spatial mode. The perturbation is used in two different ways: A global perturbation is realized by forcing an electric current through the one-dimensional system, whereas the local perturbation is performed by modulating concentrations of the autocatalyst at the boundaries. Only the global method enhances the contribution of the dominant mode to the total fluctuation energy. On the other hand, the local method leads to simple bulk oscillation of the entire system.

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