scholarly journals Exponential Stability in Hyperbolic Thermoelastic Diffusion Problem with Second Sound

2011 ◽  
Vol 2011 ◽  
pp. 1-21 ◽  
Author(s):  
Moncef Aouadi
Keyword(s):  
Exponential Stability ◽  
Classical Theory ◽  
Hyperbolic Equations ◽  
Propagation Speed ◽  
Diffusion Problem ◽  
Second Sound ◽  
Thermoelastic Diffusion ◽  
Infinite Propagation Speed ◽  
And Diffusion ◽  
Cattaneo’S Law

We consider a thermoelastic diffusion problem in one space dimension with second sound. The thermal and diffusion disturbances are modeled by Cattaneo's law for heat and diffusion equations to remove the physical paradox of infinite propagation speed in the classical theory within Fourier's law. The system of equations in this case is a coupling of three hyperbolic equations. It poses some new analytical and mathematical difficulties. The exponential stability of the slightly damped and totally hyperbolic system is proved. Comparison with classical theory is given.

Spectral and numerical analysis for a thermoelastic problem with double porosity and second sound

2021 ◽  
pp. 1-38
Author(s):  
Moncef Aouadi ◽  
Imed Mahfoudhi ◽  
Taoufik Moulahi
Keyword(s):  
Stability Result ◽  
Propagation Speed ◽  
Double Porosity ◽  
Thermoelastic Problem ◽  
Physical Parameters ◽  
Second Sound ◽  
Evolution Law ◽  
Infinite Propagation Speed ◽  
Generalized Eigenfunctions ◽  
Chebyshev Spectral Method

We study some spectral and numerical properties of the solutions to a thermoelastic problem with double porosity. The model includes Cattaneo-type evolution law for the heat flux to remove the physical paradox of infinite propagation speed of the classical Fourier’s law. Firstly, we prove that the operator determined by the considered problem has compact resolvent and generates a C 0 -semigroup in an appropriate Hilbert space. We also show that there is a sequence of generalized eigenfunctions of the linear operator that forms a Riesz basis. By a detailed spectral analysis, we obtain the expressions of the spectrum and we deduce that the spectrum determined growth condition holds. Therefore we prove that the energy of the considered problem decays exponentially to a rate determined explicitly by the physical parameters. Finally, some numerical simulations based on Chebyshev spectral method for spatial discretization are given to confirm the exponential stability result and to show the distribution of the eigenvalues and the variables of the problem.

scholarly journals Turbulence and diffusion in the lower atmosphere

1946 ◽  
Vol 186 (1004) ◽  
pp. 20-35 ◽  
Keyword(s):  
Water Vapour ◽  
Atmospheric Turbulence ◽  
Classical Theory ◽  
Quantitative Approach ◽  
Lower Atmosphere ◽  
Mixing Length ◽  
Self Consistent ◽  
Consistent Treatment ◽  
And Diffusion ◽  
Turbulence And Diffusion

The only existing theory of atmospheric turbulence which is capable of giving a quantitative approach to the complex problems of diffusion in the lower atmosphere is the classical theory in which it is generally assumed that the effect of eddies in the atmosphere is completely analogous to that of molecules in a gas apart from a difference of scale. This assumption, which later evidence has shown to be incorrect, is not essential to the theory, and in the present paper is replaced by the assumption that the mixing length of an eddy increases with both height above and nature of the earth’s surface . With this assumption a self-consistent treatment of diffusion is developed which is able to account quantitatively for such meteorological phenomena as the distribution of water vapour over land and sea (including evaporation from the oceans) and the diffusion of smoke near the ground. The treatment is mainly confined to diffusion in an adiabatic atmosphere.

Global well-posedness and infinite propagation speed for the N − abc family of Camassa–Holm type equation with both dissipation and dispersion

2020 ◽  
Vol 61 (7) ◽  
pp. 071502
Author(s):  
Zaiyun Zhang ◽  
Zhenhai Liu ◽  
Youjun Deng ◽  
Chuangxia Huang ◽  
Shiyou Lin ◽  
...  
Keyword(s):  
Type Equation ◽  
Propagation Speed ◽  
Well Posedness ◽  
Infinite Propagation Speed

Exponential stability of a flexible structure with second sound

2019 ◽  
Vol 122 (1) ◽  
pp. 71-79 ◽  
Author(s):  
Wenjun Liu ◽  
Jiangyong Yu ◽  
Gang Li
Keyword(s):  
Exponential Stability ◽  
Flexible Structure ◽  
Second Sound

Role of facilitated diffusion of calcium by calbindin in intestinal calcium absorption

1992 ◽  
Vol 262 (2) ◽  
pp. C517-C526 ◽  
Author(s):  
J. J. Feher ◽  
C. S. Fullmer ◽  
R. H. Wasserman
Keyword(s):  
Negative Feedback ◽  
Calcium Absorption ◽  
Feedback Inhibition ◽  
Basolateral Membrane ◽  
Reaction Diffusion ◽  
Diffusion Problem ◽  
Facilitated Diffusion ◽  
Calbindin D9k ◽  
And Diffusion

Computer simulations of transcellular Ca2+ transport in enterocytes were carried out using the simulation program SPICE. The program incorporated a negative-feedback entry of Ca2+ at the brush-border membrane that was characterized by an inhibitor constant of 0.5 microM cytosolic Ca2+ concentration ([Ca2+]). The basolateral Ca(2+)-ATPase was simulated by a four-step mechanism that resulted in Michaelis-Menten kinetics with a Michaelis constant of 0.24 microM [Ca2+]. The cytosolic diffusion of Ca2+ was simulated by dividing the cytosol into 10 slabs of equal width. Ca2+ binding to calbindin-D9K was simulated in each slab, and diffusion of free Ca2+, free calbindin, and Ca(2+)-laden calbindin was simulated between each slab. The cytosolic [Ca2+] of the simulated cells was regulated within the physiological range. Calbindin-D9K reduced the cytosolic [Ca2+] gradient, increased Ca2+ entry into the cell by removing the negative-feedback inhibition of Ca2+ entry, increased cytosolic Ca2+ flow, and increased the efflux of Ca2+ across the basolateral membrane by increasing the free [Ca2+] immediately adjacent to the pump. The enhancement of transcellular Ca2+ transport was nearly linearly dependent on calbindin-D9K concentration. The values of the dissociation constant (Kd) for calbindin-D9K were previously obtained experimentally in the presence and absence of KCl. Calbindin with the Kd obtained in the presence of KCl enhanced the simulated Ca2+ transport more than with the Kd obtained in the absence of KCl. This result suggests that the physiological Kd of calbindin is optimal for the enhancement of transcellular Ca2+ transport. The simulated Ca2+ flow was less than that predicted from the "near-equilibrium" analytic solution of the reaction-diffusion problem.

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