Determination of the Reaction Function in a Reaction-Diffusion Parabolic Problem

1994 ◽  
Vol 116 (4) ◽  
pp. 1041-1044 ◽  
Author(s):  
H. R. B. Orlande ◽  
M. N. O¨zis¸ik
1997 ◽  
Vol 36 (1) ◽  
pp. 271-277 ◽  
Author(s):  
Qin Zhou ◽  
Paul L. Bishop

Biofiltration is a popular method for removing volatile organic compounds (VOCs). One promising medium for biofilters is biomass encapsulated gel beads. Like any other biodegradation system, oxygen concentration is an important factor affecting microbial activities in gel beads and thus the VOC removal efficiency. This paper summarizes the studies on oxygen distribution and diffusivity in k-carrageenan gel beads using oxygen microelectrodes to measure oxygen profiles. By using a reaction-diffusion model and the concentration measurements obtained, a homogeneous diffusivity constant and an oxygen consumption rate constant in k-carrageenan gel beads were estimated. The estimated oxygen diffusivity in the gel bead is 46.3% of the value in water when the bead is immersed in water and 53.9% that of water when the bead is in air with a thin liquid film surrounding it. To provide more information for the design and operation of biofilters using biomass-loaded gel beads, we also investigated and report on effects of biomass immobilization time, TCE influent concentration and TCE gas flow rate on oxygen concentrations in the gel bead.


2016 ◽  
Vol 6 (4) ◽  
pp. 434-447 ◽  
Author(s):  
M. Mbehou ◽  
R. Maritz ◽  
P.M.D. Tchepmo

AbstractThis article is devoted to the study of the finite element approximation for a nonlocal nonlinear parabolic problem. Using a linearised Crank-Nicolson Galerkin finite element method for a nonlinear reaction-diffusion equation, we establish the convergence and error bound for the fully discrete scheme. Moreover, important results on exponential decay and vanishing of the solutions in finite time are presented. Finally, some numerical simulations are presented to illustrate our theoretical analysis.


2015 ◽  
Vol 9 (1) ◽  
pp. 103-119 ◽  
Author(s):  
Soon-Yeong Chung ◽  
Jae-Hwang Lee

In this paper, we discuss the conditions under which blow-up occurs for the solutions of reaction-diffusion equations on networks. The analysis of this class of problems includes the existence of blow-up in finite time and the determination of the blow-up time and the corresponding blow-up rate. In addition, when the solution blows up, we give estimates for the blow-up time and also provide the blow-up rate. Finally, we show some numerical illustrations which describe the main results.


Author(s):  
L. Hegedüs ◽  
M. Wittmann ◽  
N. Kirschner ◽  
Z. Noszticzius

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