scholarly journals The effect of exclusion on nonlinear reaction–diffusion system in inhomogeneous media

2014 ◽  
Vol 405 ◽  
pp. 52-62 ◽  
Author(s):  
Trilochan Bagarti ◽  
Anupam Roy ◽  
K. Kundu ◽  
B.N. Dev
Keyword(s):  
Reaction Diffusion ◽  
Inhomogeneous Media ◽  
Reaction Diffusion System ◽  
Diffusion System ◽  
Nonlinear Reaction

Image restoration and contrast enhancement based on a nonlinear reaction-diffusion mathematical model and divide & conquer technique

2021 ◽  
Vol 8 (3) ◽  
pp. 549-559
Author(s):  
K. Alaa ◽  
◽  
M. Atounti ◽  
M. Zirhem ◽  
◽  
...  
Keyword(s):  
Mathematical Model ◽  
Image Processing ◽  
High Frequency ◽  
Impulse Noise ◽  
Reaction Diffusion ◽  
Reaction Diffusion System ◽  
Diffusion System ◽  
Simple Scheme ◽  
Nonlinear Reaction ◽  
Frequency Components

In this article, we present a new algorithm for digital image processing noised by mixed Gaussian-impulse noise. Our mathematical model is based on the divide-conquer technique coupled with a reaction-diffusion system. We first decompose our image into low and high-frequency components by convolving each with a predefined convolutional filter. Further, we use a simple scheme of different weights to integrate and collect these processed sub-images into a filtered image. Finally, we apply our Reaction-Diffusion system to increase the contrast in the image. A number of experimental results are described to illustrate the performance of our algorithm and show that it is very effective in eliminating mixed Gaussian-impulse noise, increasing the contrast of the image and preserving the edges.

scholarly journals Local controllability of reaction-diffusion systems around nonnegative stationary states

2020 ◽  
Vol 26 ◽  
pp. 55
Author(s):  
Kévin Le Balc’h
Keyword(s):  
Reaction Diffusion ◽  
Reaction Diffusion System ◽  
Diffusion System ◽  
Local Controllability ◽  
Laplacian Operator ◽  
Stationary States ◽  
Inverse Mapping ◽  
Smooth Bounded Domain ◽  
Reaction Diffusion Systems ◽  
Nonlinear Reaction

We consider a n × n nonlinear reaction-diffusion system posed on a smooth bounded domain Ω of ℝN. This system models reversible chemical reactions. We act on the system through m controls (1 ≤ m < n), localized in some arbitrary nonempty open subset ω of the domain Ω. We prove the local exact controllability to nonnegative (constant) stationary states in any time T > 0. A specificity of this control system is the existence of some invariant quantities in the nonlinear dynamics that prevents controllability from happening in the whole space L∞(Ω)n. The proof relies on several ingredients. First, an adequate affine change of variables transforms the system into a cascade system with second order coupling terms. Secondly, we establish a new null-controllability result for the linearized system thanks to a spectral inequality for finite sums of eigenfunctions of the Neumann Laplacian operator, due to David Jerison, Gilles Lebeau and Luc Robbiano and precise observability inequalities for a family of finite dimensional systems. Thirdly, the source term method, introduced by Yuning Liu, Takéo Takahashi and Marius Tucsnak, is revisited in a L∞-context. Finally, an appropriate inverse mapping theorem in suitable spaces enables to go back to the nonlinear reaction-diffusion system.

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