scholarly journals Wavefronts for degenerate diffusion-convection reaction equations with sign-changing diffusivity

2021 ◽  
Vol 0 (0) ◽  
pp. 0
Author(s):  
Diego Berti ◽  
Andrea Corli ◽  
Luisa Malaguti
Keyword(s):  
Degenerate Diffusion ◽  
Diffusion Convection ◽  
Reaction Equations

On the Diffusion-Convection-Reaction Equations

1999 ◽  
Vol 60 (3) ◽  
pp. 207-210 ◽  
Author(s):  
S A El-Wakil ◽  
A Elhanbaly ◽  
M A Abdou
Keyword(s):  
Diffusion Convection ◽  
Reaction Equations

Three-dimensional solutions of nonlinear degenerate diffusion-convection processes

1991 ◽  
Vol 2 (2) ◽  
pp. 171-187 ◽  
Author(s):  
Gérard Gagneux ◽  
Monique Madaune-Tort
Keyword(s):  
Porous Medium ◽  
Three Dimensional ◽  
Theoretical Modelling ◽  
Degenerate Diffusion ◽  
Qualitative Properties ◽  
Hydrocarbon Component ◽  
Secondary Recovery ◽  
Diffusion Convection ◽  
Applied Fields ◽  
Nonlinear Degenerate

The main objective of this work is to present, for practical use, some original results about several qualitative properties of the solutions of a large class of degenerate diffusion-convection equations arising from fluid mechanics. Current interest in models of the simultaneous motion of two immiscible incompressible liquids results from its significance for many applied fields such as, for instance, the theoretical modelling of oil reservoirs where the pores of a threedimensional porous medium contain some hydrocarbon component (oil). In secondary recovery, a second inexpensive fluid (water) is injected into the porous medium in order to push the oil towards the producing wells.

scholarly journals Numerical algorithms for solving the optimal control problem of simple bioreactors

2019 ◽  
Vol 24 (4) ◽  
Author(s):  
Raimondas Čiegis ◽  
Remigijus Čiegis
Keyword(s):  
Nonlinear Diffusion ◽  
Finite Difference Methods ◽  
Numerical Algorithms ◽  
External Boundary ◽  
Enzymatic Conversion ◽  
Control Loop ◽  
Potential Accuracy ◽  
Difference Methods ◽  
Diffusion Convection ◽  
Reaction Equations

The modified nonlocal feedback controller is used to control the production of drugs in a simple bioreactor. This bioreactor is based on the enzymatic conversion of substrate into the required product. The dynamics of this device is described by a system of two nonstationary nonlinear diffusion–convection–reaction equations. The analysis of the influence of the convection transport is one the aims of this paper. The control loop is defined using the relation, which shows how the amount of the drug produced in the bioreactor and delivered into a human body depends on the substrate concentration specified on the external boundary of the bioreactor. The system of PDEs is solved by using the finite volume and finite difference methods, the control loop parameters are defined from the analysis of stationary linearized equations. The second aim of this paper is to solve the inverse problem and to determine optimal boundary conditions. These results enable us to estimate the potential accuracy of the proposed devices.  

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