advection-diffusion-reaction system
Asymptotic stability of a coupled advection-diffusion-reaction system arising in bioreactor processes
... two advection-diffusion-reaction equations with Danckwerts boundary conditions, which models the interaction between a microbial population ...This system exhibits, under suitable conditions, ...
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Reduced-order minimum time control of advection-reaction-diffusion systems via dynamic programming.
... II. D ISCRETIZATION AND MODEL REDUCTION In this section, we present a semi-discretization of the reaction-diffusion-advection equation (I.1) resulting in a finite-dimensional dynamical system. ...
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Simulation of a time dependent advection-reaction-diffusion problem using operator splitting and discontinuous Galerkin methods with application to plant root growth
... root system develop- ment. One can notice the diffusion of the apices in the soil and also the transport of the apices from the top to the bottom of the soil ...root system growth can last for a long ...
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Asymptotic analysis of an advection-diffusion equation and application to boundary controllability
... that system (1) can be seen as a simple example of complex models where the diffusion coefficient is very small compared to the ...Stokes system where ε stands for the viscosity ...
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Numerical analysis of the advection-diffusion of a solute in random media
... = max{kf k ∞ , kf 0 k ∞ , ..., kf (k) k ∞ , kf (k) k C 0,α b }. The numerical analysis of the above algorithm requires the solution of (2) to be su - ciently regular with respect to x ∈ O. Unfortunately, this is not the ...
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Information denoising and quantization by diffusion reaction model
... where G t (x) = (1/2πt) exp(−x 2 /2t) is the gaussian function. This diffusion process kind clearly contradict the requierement of the quantization effect. Indeed, in ordre to creat discontinuities, the ...
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Hele-Shaw limit for a system of two reaction-(cross-)diffusion equations for living tissues
... The evolution of solutions to system ( 1 ) and the corresponding pressure are shown, for two values of γ, in Figure 1 . Functions are F 1 (p) = (1 − K p ), with K = 3, G 2 (p) = (1 − p) and G 1 (p) = F 2 (p) = (1 ...
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Transition fronts for periodic bistable reaction-diffusion equations
... the reaction terms f (x, u) and by using different types of arguments, we proved several existence results of pulsating fronts with nonzero or zero speeds when the spatial period L is small or large (we will come ...
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Asymptotic behaviour of reversible chemical reaction-diffusion equations
... reversible reaction-diffusion chemical reaction between three species such that the water has to appear twice for the ...a diffusion term will be ...the reaction. If the reaction ...
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Coupled gas flow, diffusion and reaction in a ppb-level Sn0₂-NiO formaldehyde sensor system
... of system design, the sensor was integrated with an upstream preconcentrator unit, a porous solid region of packed powder of a carbon molecular sieve material (Carboxen 1018, Supelco), a highly efficient ...
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One-dimensional linear advection–diffusion equation: Analytical and finite element solutions
... homogeneous Dirichlet boundary conditions as this is a meaning- ful test for established or novel discrete schemes. For high Rey- nolds number flows the advection is dominating diffusion but the presence of ...
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Multiple-Relaxation-Time Lattice Boltzmann scheme for fractional advection–diffusion equation
... involving general α α α provided the skewness parameter p p p takes the value 1 or 0 with, moreover, specific source term S c and initial data. Though Eq. (1) with S c = 0 constitutes an important simple case, it does ...
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Persistence and propagation in periodic reaction-diffusion models
... the diffusion matrix D is constant and equal to the identity matrix D = I and we therefore only focus on the role of the intrinsic growth rate coefficient ...
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Shape optimization and spatial heterogeneity in reaction-diffusion equations
... Motivations Reaction-diffusion equations have drawn a lot of attention from the mathematical community over the last decades, but most usually in spatially homogeneous setting, while the lit- erature ...
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Asymptotic analysis of an advection-diffusion equation involving interacting boundary and internal layers
... 0 (0)) leads to an error of order ε 3/2 . Assuming the data v and y 0 in C 4 (0, T ) and C 4 (0, 1), respectively, we construct in this work an explicit C 1 -approximation of y ε , leading to error estimates in L ∞ (0, T ...
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Homogenization of advection-diffusion and solid diffusion in poroelastic media for modelling transport of soluble factors in biological tissues
... la diffusion de documents scientifiques de niveau recherche, publiés ou non, émanant des établissements d’enseignement et de recherche français ou étrangers, des laboratoires publics ou ...
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A fractional reaction–diffusion description of supply and demand
... non-Gaussian diffusion is still topical in many different fields such as statistical physics, condensed matter physics or biology – as testified by the present special issue of ...fractional diffusion to ...
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On the controllability of an advection-diffusion equation with respect to the diffusion parameter: Asymptotic analysis and numerical simulations
... The advection-diffusion equation y ε t − εy ε xx + M y x ε = 0, (x, t) ∈ (0, 1) × (0, T ) is null controllable for any strictly positive values of the diffusion coefficient ε and of the ...
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A statistical-reaction-diffusion approach for analyzing expansion processes
... the reaction-diffusion model can be replaced by other types of models such as individual based models (Gross et ...the reaction-diffusion approach was encouraged by computational speed ...
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State-constrained controllability of linear reaction-diffusion systems
... de diffusion diagonales avec contrainte de positivité “approchée”, et un autre, plus fort, avec une contrainte de positivité “exacte”, dans le cas où les coefficients de diffusion sont identiques et où les ...
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