Liesegang Phenomenon of Liquid Metals on Au Film
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DOI: 10.1002/adma.202209392
Abstract: Room temperature liquid metals (LM) such as gallium (Ga) own the potential to react with specific materials which would incubate new application categories. Here, diverse self‐organized ring patterns due to nonequilibrium reaction‐diffusion and spreading‐limitation of… read more here.
Keywords: liquid metals; film; reaction diffusion; liesegang ... See more keywords
Boundary stabilization of semi‐linear time fractional reaction–diffusion systems with delays
Sign Up to like & getrecommendations! Published in 2024 at "Asian Journal of Control"
DOI: 10.1002/asjc.3556
Abstract: This paper examines the stabilization results for a class of semi‐linear time fractional reaction–diffusion partial differential equations (PDEs) with state delay using the backstepping method. The main goal is to design the boundary control for… read more here.
Keywords: reaction; semi linear; linear time; time fractional ... See more keywords
Single blowup point for a semilinear reaction‐diffusion system
Sign Up to like & getrecommendations! Published in 2018 at "Mathematische Nachrichten"
DOI: 10.1002/mana.201400335
Abstract: Throughout this paper, we investigate the blowup set for the semilinear reaction‐diffusion system ut=Δu+f(u,v),x∈Ω,t>0,vt=Δv+g(u,v),x∈Ω,t>0,u(x,t)=v(x,t)=0,x∈∂Ω,t>0,u(x,0)=u0(x),v(x,0)=v0(x),x∈Ω,where Ω=BR:={x∈Rn;|x| read more here.
Keywords: semilinear reaction; reaction diffusion; diffusion system; blowup ... See more keywords
Solitons for a generalized reaction–diffusion equation with the higher‐order power‐law nonlinearity in (1+1)‐ and (2+1)‐dimensional systems
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DOI: 10.1002/mma.10313
Abstract: For the systems modeled by a generalized reaction–diffusion equation with the higher‐order quintic nonlinearity, we explore the soliton dynamics via the F‐expansion method. By the novel F‐base function ansatz, we first derived the bright soliton… read more here.
Keywords: nonlinearity; diffusion equation; reaction diffusion;
Turing Instability of Spatially Homogeneous Periodic Solutions in a Reaction–Diffusion Bimolecular Model
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DOI: 10.1002/mma.10971
Abstract: In recent years, Turing instability in coupled reaction–diffusion systems has garnered extensive attention from numerous researchers. Nevertheless, the majority of extant studies primarily concentrate on the Turing instability of constant steady states, with comparatively few… read more here.
Keywords: turing instability; diffusion; periodic solutions; reaction diffusion ... See more keywords
A Stable Hybridized Discontinuous Galerkin Method for Solving Some Nonlinear m‐Component Reaction–Diffusion Systems
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DOI: 10.1002/mma.11034
Abstract: In this paper, we present a stable numerical scheme for solving two‐dimensional m$$ m $$ ‐component reaction–diffusion systems. The proposed approach utilizes the backward Euler method for temporal discretization and the hybridized discontinuous Galerkin (HDG)… read more here.
Keywords: method; component reaction; diffusion systems; reaction diffusion ... See more keywords
A singular reaction-diffusion equation associated with brain lactate kinetics
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DOI: 10.1002/mma.4150
Abstract: Our aim in this paper is to study the well-posedness of a singular reaction-diffusion equation which is related with brain lactate kinetics, when spatial diffusion is taken into account. Copyright © 2016 John Wiley &… read more here.
Keywords: diffusion; brain lactate; singular reaction; reaction diffusion ... See more keywords
Dissipativity and synchronization control of fractional‐order memristive neural networks with reaction‐diffusion terms
Sign Up to like & getrecommendations! Published in 2019 at "Mathematical Methods in the Applied Sciences"
DOI: 10.1002/mma.5873
Abstract: This paper deals with the dissipativity and synchronization control of fractional‐order memristive neural networks (FOMNNs) with reaction‐diffusion terms. By means of fractional Halanay inequality, Wirtinger inequality, and Lyapunov functional, some sufficient conditions are provided to… read more here.
Keywords: diffusion terms; dissipativity synchronization; reaction diffusion;
Nonnegative solutions to reaction–diffusion system with cross‐diffusion and nonstandard growth conditions
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DOI: 10.1002/mma.6401
Abstract: We establish the existence of nonnegative weak solutions to nonlinear reaction–diffusion system with cross‐diffusion and nonstandard growth conditions subject to the homogeneous Neumann boundary conditions. We assume that the diffusion operators satisfy certain monotonicity condition… read more here.
Keywords: nonstandard growth; diffusion; diffusion system; growth conditions ... See more keywords
Numerical solutions for the reaction–diffusion, diffusion‐wave, and Cattaneo equations using a new operational matrix for the Caputo–Fabrizio derivative
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DOI: 10.1002/mma.6517
Abstract: In this research work, we study the model of nonlinear reaction–diffusion equation, diffusion‐wave equation, and Cattaneo equation with the help of a numerical method in which time‐fractional derivative is of Caputo–Fabrizio type (C‐F). First, we… read more here.
Keywords: operational matrix; diffusion; equation; diffusion wave ... See more keywords
Global synchronization of fractional‐order and integer‐order N component reaction diffusion systems: Application to biochemical models
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DOI: 10.1002/mma.6807
Abstract: This study considers the problem of control and synchronization between fractional‐order and integer‐order, N‐components reaction‐diffusion systems with nonidentical coefficients and different nonlinear parts. The control scheme is designed using the Lyapunov direct method. The results… read more here.
Keywords: integer order; order; fractional order; reaction diffusion ... See more keywords