Asymptotic stability of a coupled advection-diffusion-reaction system arising in bioreactor processes
Texte intégral
Figure
![Figure 2. Graphical plots of functions β 1 (Da, Th B ) and f Th B (Da) (described in Definitions 3.4 and 3.11, respectively) for Th B ∈ { 1 5 , 1, 5} and Da ∈ [0, 2].](https://thumb-eu.123doks.com/thumbv2/123doknet/14373130.504668/19.918.219.698.195.432/figure-graphical-plots-functions-da-described-definitions-respectively.webp)
![Figure 3. Comparison between the functions Da W (2.4) (Th B , 0.5), Da W (2.4) (Th B , 0.5) and Dac W (2.4) (Th B , 0.5) (depicted with solid, dot-ted and dashed lines, respectively), when Th B ∈ [5 · 10 −3 , 5 · 10 3 ].](https://thumb-eu.123doks.com/thumbv2/123doknet/14373130.504668/21.918.294.618.192.457/figure-comparison-functions-depicted-solid-dashed-lines-respectively.webp)
![Figure 6. Comparisong between log(Da W (2.4) (Th B , 0.5)), log(Da NW (A2),(2.4) (Th B )) (solid lines) and constant values log(Da W (1.2) (0.5)) = log(2), log(Da NW (A2),(1.2) ) = 0 (dashed line) when Th B ∈ [5 × 10 −3 , 1.5 × 10 2 ].](https://thumb-eu.123doks.com/thumbv2/123doknet/14373130.504668/24.918.251.670.184.548/figure-comparisong-solid-lines-constant-values-dashed-line.webp)
Documents relatifs
Keywords: Asymptotic analysis, partial dierential equations, anomalous diusion, structured equations, relative entropy, Hamilton-Jacobi equations, subdiusion in
To give a qualitative picture, we report in figure 6 the final numerical solutions after one full turn obtained using the SD-ROM with online a-posteriori stabilization for r = 30,
We provide in this paper the complete asymtotically optimized closed form transmission conditions for optimized Schwarz waveform relaxation algorithms applied to advection
and Langlais M., 2010, Proposition of a conceptual density based model to describe fine roots networks in tree root system, Plant Modelling Applications 09 proceedings.
Keywords: Age-space-structured PDE, Reaction-diffusion system with delay, Difference equation, Dirichlet boundary condition, Existence and uniqueness of positive steady state,
Our propose is to study monotone traveling waves for the coupled reaction- diffusion and difference system (8) by reducing the problem to the existence of an admissible pair of
The results of the current research can be used in several areas of applied mathematics, especially when the system equations originate from mathematical models of real systems
The extension to advection-diffusion-reaction equations entails several new ideas: (i) We de- vise a local reconstruction of the advective derivative from cell- and face-based
