scholarly journals A Weak Comparison Principle for Reaction-Diffusion Systems

2012 ◽  
Vol 2012 ◽  
pp. 1-30 ◽  
Author(s):  
José Valero
Keyword(s):  
Comparison Principle ◽  
Reaction Diffusion ◽  
Volterra System ◽  
Uniqueness Of Solutions ◽  
Reaction Diffusion Systems ◽  
System A ◽  
Diffusion Systems ◽  
Bounded Functions ◽  
Weak Comparison Principle ◽  
Generalized Logistic Equation

We prove a weak comparison principle for a reaction-diffusion system without uniqueness of solutions. We apply the abstract results to the Lotka-Volterra system with diffusion, a generalized logistic equation, and to a model of fractional-order chemical autocatalysis with decay. Moreover, in the case of the Lotka-Volterra system a weak maximum principle is given, and a suitable estimate in the space of essentially bounded functionsL∞is proved for at least one solution of the problem.

scholarly journals Novel numerical analysis for nonlinear advection–reaction–diffusion systems

Open Physics ◽  
2020 ◽  
Vol 18 (1) ◽  
pp. 112-125
Author(s):  
Naveed Shahid ◽  
Nauman Ahmed ◽  
Dumitru Baleanu ◽  
Ali Saleh Alshomrani ◽  
Muhammad Sajid Iqbal ◽  
...  
Keyword(s):  
Existence And Uniqueness ◽  
Numerical Scheme ◽  
Continuous System ◽  
Reaction Diffusion ◽  
Uniqueness Of Solutions ◽  
Reaction Diffusion Systems ◽  
System A ◽  
Diffusion Systems ◽  
Advection Term ◽  
Nonlinear Advection

AbstractIn this article, a numerical model for a Brusselator advection–reaction–diffusion (BARD) system by using an elegant numerical scheme is developed. The consistency and stability of the proposed scheme is demonstrated. Positivity preserving property of the proposed scheme is also verified. The designed scheme is compared with the two well-known existing classical schemes to validate the certain physical properties of the continuous system. A test problem is also furnished for simulations to support our claim. Prior to computations, the existence and uniqueness of solutions for more generic problems is investigated. In the underlying system, the nonlinearities depend not only on the desired solution but also on the advection term that reflects the pivotal importance of the study.

scholarly journals Cell-sized confinement controls generation and stability of a protein wave for spatiotemporal regulation in cells

eLife ◽  
2019 ◽  
Vol 8 ◽  
Author(s):  
Shunshi Kohyama ◽  
Natsuhiko Yoshinaga ◽  
Miho Yanagisawa ◽  
Kei Fujiwara ◽  
Nobuhide Doi
Keyword(s):  
Volume Ratio ◽  
Reaction Diffusion ◽  
Live Cells ◽  
Confined Space ◽  
Bacterial Cell Division ◽  
Division Plane ◽  
Reaction Diffusion Systems ◽  
System A ◽  
Spatiotemporal Regulation ◽  
Diffusion Systems

The Min system, a system that determines the bacterial cell division plane, uses changes in the localization of proteins (a Min wave) that emerges by reaction-diffusion coupling. Although previous studies have shown that space sizes and boundaries modulate the shape and speed of Min waves, their effects on wave emergence were still elusive. Here, by using a microsized fully confined space to mimic live cells, we revealed that confinement changes the conditions for the emergence of Min waves. In the microsized space, an increased surface-to-volume ratio changed the localization efficiency of proteins on membranes, and therefore, suppression of the localization change was necessary for the stable generation of Min waves. Furthermore, we showed that the cell-sized space strictly limits parameters for wave emergence because confinement inhibits both the instability and excitability of the system. These results show that confinement of reaction-diffusion systems has the potential to control spatiotemporal patterns in live cells.

THE CONVERGENCE OF A CLASS OF QUASIMONOTONE REACTION–DIFFUSION SYSTEMS

2001 ◽  
Vol 64 (2) ◽  
pp. 395-408 ◽  
Author(s):  
YI WANG ◽  
JIFA JIANG
Keyword(s):  
Differential Equation ◽  
Reaction Diffusion ◽  
Initial Boundary ◽  
Equation System ◽  
Continuous Functions ◽  
Differential Equation System ◽  
Volterra System ◽  
Reaction Diffusion Systems ◽  
Initial Boundary Problem ◽  
Diffusion Systems

It is proved that every solution of the Neumann initial-boundary problem[formula here]converges to some equilibrium, if the system satisfies (i) ∂Fi/∂uj [ges ] 0 for all 1 [les ] i ≠ j [les ] n, (ii) F(u * g(s)) [ges ] h(s) [midast ] F(u) whenever u ∈ ℝn+ and 0 [les ] s [les ] 1, where x * y = (x1y1, …, xnyn) and g, h : [0, 1] → [0, 1]n are continuous functions satisfying gi(0) = hi(0) = 0, gi(1) = hi(1) = 1, 0 < gi(s); hi(s) < 1 for all s ∈ (0, 1) and i = 1, 2, …, n, and (iii) the solution of the corresponding ordinary differential equation system is bounded in ℝn+. We also study the convergence of the solution of the Lotka–Volterra system[formula here]where ri > 0, α [ges ] 0, and aij [ges ] 0 for i ≠ j.

A CMOS REACTION–DIFFUSION DEVICE USING MINORITY-CARRIER DIFFUSION IN SEMICONDUCTORS

2007 ◽  
Vol 17 (05) ◽  
pp. 1713-1719 ◽  
Author(s):  
MOTOYOSHI TAKAHASHI ◽  
TETSUYA ASAI ◽  
TETSUYA HIROSE ◽  
YOSHIHITO AMEMIYA
Keyword(s):  
Minority Carrier ◽  
Reaction Diffusion ◽  
Natural World ◽  
Dissipative Structures ◽  
Carrier Diffusion ◽  
Reaction Diffusion Systems ◽  
System A ◽  
Diffusion Systems ◽  
Chemical Complex ◽  
Dynamic Phenomena

We propose a CMOS device that is analogous to the reaction–diffusion system, a chemical complex system that produces various dynamic phenomena in the natural world. This electrical reaction–diffusion device consists of an array of pn junctions that are operated by CMOS reaction circuits and interact with each other through minority-carrier diffusion. Computer simulations reveal that the device can produce animated spatiotemporal carrier concentration patterns, e.g. expanding circular patterns and rotating spiral patterns that correspond to the dissipative structures produced by chemical reaction–diffusion systems.

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