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Global Renormalised Solutions and Equilibration of Reaction–Diffusion Systems with Nonlinear Diffusion
The global existence of renormalised solutions and convergence to equilibrium for reaction–diffusion systems with nonlinear diffusion are...
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Turing Pattern Formation in Reaction-Cross-Diffusion Systems with a Bilayer Geometry
Conditions for self-organisation via Turing’s mechanism in biological systems represented by reaction-diffusion or reaction-cross-diffusion models...
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Reaction-Diffusion Problems
In this chapter, we start by investigating the adsorption-desorptionAdsorption-desorption (process, phenomenon, boundary conditions, etc.) Boundary...
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A time independent least squares algorithm for parameter identification of Turing patterns in reaction–diffusion systems
Turing patterns arising from reaction–diffusion systems such as epidemic, ecology or chemical reaction models are an important dynamic property....
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Existence of Solution of a Free Boundary Problem for Reaction–Diffusion Systems
In this paper, we prove the existence of a solution of a novel free boundary problem for reaction-diffusion systems describing growth of biological...
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Delayed blow-up and enhanced diffusion by transport noise for systems of reaction–diffusion equations
This paper is concerned with the problem of regularization by noise of systems of reaction–diffusion equations with mass control. It is known that strong...
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General conditions for Turing and wave instabilities in reaction -diffusion systems
Necessary and sufficient conditions are provided for a diffusion-driven instability of a stable equilibrium of a reaction–diffusion system with n ...
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Existence, Asymptotics, and Lyapunov Stability of Solutions of Periodic Parabolic Problems for Tikhonov-Type Reaction–Diffusion Systems
AbstractWe study a new class of time-periodic solutions of singularly perturbed systems of reaction–diffusion equations in the case of a fast and a...
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Concentration-Dependent Domain Evolution in Reaction–Diffusion Systems
Pattern formation has been extensively studied in the context of evolving (time-dependent) domains in recent years, with domain growth implicated in...
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Analysis of mass controlled reaction–diffusion systems with nonlinearities having critical growth rates
We analyze semilinear reaction–diffusion systems that are mass controlled, and have nonlinearities that satisfy critical growth rates. The systems...
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Observer-based piecewise control of reaction–diffusion systems with the non-collocated output feedback
This paper mainly deals with an observer-based control problem for the nonlinear reaction–diffusion systems subject to non-collocated output...
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Discontinuous stationary solutions to certain reaction-diffusion systems
Systems consisting of a single ordinary differential equation coupled with one reaction-diffusion equation in a bounded domain and with the Neumann...
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Oscillatory Motions of Multiple Spikes in Three-Component Reaction–Diffusion Systems
For three specific singular perturbed three-component reaction–diffusion systems that admit N -spike solutions in one of the components on a finite...
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Propagation Dynamics for Time–Space Periodic and Partially Degenerate Reaction–Diffusion Systems with Time Delay
This paper is concerned with the propagation dynamics of a large class of time–space periodic and partially degenerate reaction–diffusion systems...
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Edge of Chaos in Reaction-Diffusion System with Memristor Synapses
In this paper principles of local activity theory will be presented for studying complex behavior of reaction-diffusion systems. For...
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Fixed and Distributed Gene Expression Time Delays in Reaction–Diffusion Systems
Time delays, modelling the process of intracellular gene expression, have been shown to have important impacts on the dynamics of pattern formation...
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A class of fractional parabolic reaction–diffusion systems with control of total mass: theory and numerics
In this paper, we prove global-in-time existence of strong solutions to a class of fractional parabolic reaction–diffusion systems posed in a bounded...
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Exponential input-to-state stabilization of stochastic nonlinear reaction–diffusion systems with time-varying delays and exogenous disturbances via boundary control
The boundary stabilization problem of stochastic nonlinear reaction–diffusion systems (SNRDSs) with time-varying delay, exogenous disturbance, and...
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Multiplicative Control Problem for a Nonlinear Reaction–Diffusion Model
AbstractThe paper studies a multiplicative control problem for the reaction–diffusion equation in which the reaction coefficient nonlinearly depends...
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Spreading Speeds of Time-Dependent Partially Degenerate Reaction-Diffusion Systems
This paper is concerned with the spreading speeds of time dependent partially degenerate reaction-diffusion systems with monostable nonlinearity. By...