Convergence to Equilibrium in Energy-Reaction–Diffusion Systems Using Vector-Valued Functional Inequalities
Sign Up to like & getrecommendations! Published in 2018 at "Journal of Nonlinear Science"
DOI: 10.1007/s00332-017-9427-9
Abstract: We discuss how the recently developed energy dissipation methods for reaction diffusion systems can be generalized to the non-isothermal case. For this, we use concave entropies in terms of the densities of the species and… read more here.
Keywords: diffusion systems; reaction diffusion; equilibrium; energy ... See more keywords
Programming Methods for DNA-Based Reaction–Diffusion Systems
Sign Up to like & getrecommendations! Published in 2020 at "New Generation Computing"
DOI: 10.1007/s00354-020-00094-z
Abstract: In this tutorial, recent development of pattern generation algorithms based on DNA computing will be overviewed. Natural pattern generation, especially in biological organisms, are often driven by spatio-temporal chemical reactions. Various reaction–diffusion systems have been… read more here.
Keywords: diffusion; dna; diffusion systems; reaction diffusion ... See more keywords
Mathematical modelling of pattern formation in activator–inhibitor reaction–diffusion systems with anomalous diffusion
Sign Up to like & getrecommendations! Published in 2019 at "Journal of Mathematical Chemistry"
DOI: 10.1007/s10910-019-01089-y
Abstract: Auto-wave solutions in nonlinear time-fractional reaction–diffusion systems are investigated. It is shown that stability of steady-state solutions and their subsequent evolution are mainly determined by the eigenvalue spectrum of a linearized system and level of… read more here.
Keywords: diffusion; activator inhibitor; anomalous diffusion; diffusion systems ... See more keywords
Pointwise-in-space stabilization and synchronization of a class of reaction–diffusion systems with mixed time delays via aperiodically impulsive control
Sign Up to like & getrecommendations! Published in 2017 at "Nonlinear Dynamics"
DOI: 10.1007/s11071-017-3420-6
Abstract: This paper investigates the problems of pointwise-in-space stabilization and synchronization of semilinear reaction–diffusion systems with Dirichlet boundary conditions and mixed delays via impulsive control. Combining impulse time-dependent Lyapunov function/functional-based methods, descriptor system approach, the Wirtinger’s… read more here.
Keywords: space; pointwise space; diffusion systems; space stabilization ... See more keywords
An Analytical Studies of the Reaction- Diffusion Systems of Chemical Reactions
Sign Up to like & getrecommendations! Published in 2021 at "International Journal of Applied and Computational Mathematics"
DOI: 10.1007/s40819-021-01028-z
Abstract: Reaction–diffusion systems are seen in not only many fields of science but also social behaviorus. In this work, Schnakenberg, Brusselator and Lengyel–Epstein models are considered that are the best known the chemical reaction–diffusion models and… read more here.
Keywords: reaction diffusion; diffusion systems; analytical studies; diffusion ... See more keywords
Some exact time-domain results related to reversible reaction–diffusion systems
Sign Up to like & getrecommendations! Published in 2020 at "Chemical Physics"
DOI: 10.1016/j.chemphys.2020.110955
Abstract: Abstract We consider a closed two-state model that can represent reversible reaction–diffusion systems. The dynamics of the reacting species are governed by coupled Smoluchowski equations. The potential curves are assumed to be flat, and the… read more here.
Keywords: time; reversible reaction; diffusion systems; reaction diffusion ... See more keywords
Controllability of shadow reaction-diffusion systems
Sign Up to like & getrecommendations! Published in 2020 at "Journal of Differential Equations"
DOI: 10.1016/j.jde.2019.10.012
Abstract: Abstract We study the null controllability of linear shadow models for reaction-diffusion systems arising as singular limits when the diffusivity of some of the components is very high. This leads to a coupled system where… read more here.
Keywords: controllability shadow; diffusion systems; reaction diffusion; controllability ... See more keywords
Dynamics of a class of delayed reaction–diffusion systems with Neumann boundary condition
Sign Up to like & getrecommendations! Published in 2018 at "Journal of Mathematical Analysis and Applications"
DOI: 10.1016/j.jmaa.2017.09.045
Abstract: Abstract This paper considers a class of delayed reaction–diffusion systems under the Neumann boundary condition which arise in epidemiology and can describe the temporal and spatial evolutionary phenomena for the bacteria population and the human… read more here.
Keywords: class delayed; systems neumann; neumann boundary; diffusion systems ... See more keywords
Bifurcation and Pattern Symmetry Selection in Reaction-Diffusion Systems with Kinetic Anisotropy
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DOI: 10.1038/s41598-019-44303-2
Abstract: Ordering and self-organization are critical in determining the dynamics of reaction-diffusion systems. Here we show a unique pattern formation mechanism, dictated by the coupling of thermodynamic instability and kinetic anisotropy. Intrinsically different from the physical… read more here.
Keywords: kinetic anisotropy; diffusion; diffusion systems; reaction diffusion ... See more keywords
Stability for stochastic reaction–diffusion systems driven by G-Brownian motion
Sign Up to like & getrecommendations! Published in 2021 at "International Journal of Control"
DOI: 10.1080/00207179.2021.1885742
Abstract: In this paper, we deal with a class of stochastic reaction–diffusion systems driven by G-Brownian motion (G-SRDSs, in short). The criterions on quasi-surely exponential stability and finite-time st... read more here.
Keywords: diffusion systems; reaction diffusion; systems driven; brownian motion ... See more keywords
Reaction diffusion systems and extensions of quantum stochastic processes
Sign Up to like & getrecommendations! Published in 2022 at "Journal of Physics A: Mathematical and Theoretical"
DOI: 10.1088/1751-8121/acd288
Abstract: Reaction diffusion systems describe the behaviour of dynamic, interacting, particulate systems. Quantum stochastic processes generalise Brownian motion and Poisson processes, having operator valued Itô calculus machinery. Here it is shown that the three standard noises… read more here.
Keywords: diffusion systems; quantum stochastic; stochastic processes; reaction diffusion ... See more keywords