scholarly journals Stability of pyramidal traveling fronts in the degenerate monostable and combustion equations Ⅰ

2017 ◽  
Vol 37 (5) ◽  
pp. 2395-2430 ◽  
Author(s):  
Zhen-Hui Bu ◽  
◽  
Zhi-Cheng Wang
Keyword(s):  
Traveling Fronts ◽  
Combustion Equations

scholarly journals Multidimensional stability of pyramidal traveling fronts in degenerate Fisher-KPP monostable and combustion equations

2021 ◽  
Vol 0 (0) ◽  
pp. 0
Author(s):  
Denghui Wu ◽  
Zhen-Hui Bu
Keyword(s):  
Comparison Principle ◽  
Initial Perturbation ◽  
Three Dimensional ◽  
Reaction Diffusion ◽  
Reaction Diffusion Equations ◽  
Diffusion Equations ◽  
Asymptotically Stable ◽  
Traveling Fronts ◽  
Bounded Perturbations ◽  
Combustion Equations

<p style='text-indent:20px;'>In this paper, multidimensional stability of pyramidal traveling fronts are studied to the reaction-diffusion equations with degenerate Fisher-KPP monostable and combustion nonlinearities. By constructing supersolutions and subsolutions coupled with the comparison principle, we firstly prove that under any initial perturbation (possibly large) decaying at space infinity, the three-dimensional pyramidal traveling fronts are asymptotically stable in weighted <inline-formula><tex-math id="M1">\begin{document}$ L^{\infty} $\end{document}</tex-math></inline-formula> spaces on <inline-formula><tex-math id="M2">\begin{document}$ \mathbb{R}^{n}\; (n\geq4) $\end{document}</tex-math></inline-formula>. Secondly, we show that under general bounded perturbations (even very small), the pyramidal traveling fronts are not asymptotically stable by constructing a solution which oscillates permanently between two three-dimensional pyramidal traveling fronts on <inline-formula><tex-math id="M3">\begin{document}$ \mathbb{R}^{4} $\end{document}</tex-math></inline-formula>.</p>

Conical traveling fronts of combustion equations in R3

2020 ◽  
Vol 108 ◽  
pp. 106509
Author(s):  
Zhen-Hui Bu ◽  
Luyi Ma ◽  
Zhi-Cheng Wang
Keyword(s):  
Traveling Fronts ◽  
Combustion Equations

scholarly journals Kinetic schemes for assessing stability of traveling fronts for the Allen–Cahn equation with relaxation

2019 ◽  
Vol 141 ◽  
pp. 234-247
Author(s):  
Corrado Lattanzio ◽  
Corrado Mascia ◽  
Ramón G. Plaza ◽  
Chiara Simeoni
Keyword(s):  
Kinetic Schemes ◽  
Cahn Equation ◽  
Traveling Fronts

The New Equations for “Rate-Determining Chemisorption of Coal”

2018 ◽  
Vol 140 (11) ◽  
Author(s):  
Cemil Koyunoğlu
Keyword(s):  
Coal Combustion ◽  
Oxygen Diffusion ◽  
Coal Particle ◽  
Reaction Rate ◽  
Volatile Matter ◽  
Temperature Level ◽  
Char Combustion ◽  
Controlling Mechanism ◽  
Combustion Equations ◽  
Determining Factor

The purpose of the new formulas, Cml, CmlK, and CmlY, which express the slowest char combustion rate, is to show the controlling mechanism of single coal burning. Oxygen diffusion through the boundary layer (as a result of releasing volatile matter from coal) to the char surface is the slowest step rate and can also represent as the rate determining. This step has not yet been taken into account in the literature and may effect incomparable decisions between numerical and experimental results of coal combustion studies. In the 1920s, Wilhelm Nusselt found the coal combustion equation for a single coal, which is based on initial coal diameter, and its burning time, or Nusselt square law (NSL). Also, the burning constant in NSL expressed oxygen partial pressure and the ambient temperature level. Nevertheless, recent studies according to char combustion have explained the effect of coal density on char combustion. Consequently, to help understand the slowest rate of char combustion, NSL as well as ordinary char combustion equations can be used together to establish the rate-determining factor. For this purpose, in this study, the slowest step of the char reaction rate is given as “Cml” of stable position for single coal particle, “CmlK” and “CmlY” for a coal particle in a motion.

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