scholarly journals Infinite propagation speed of the Camassa–Holm equation

2007 ◽  
Vol 325 (2) ◽  
pp. 1468-1478 ◽  
Author(s):  
Jonatan Lenells
Keyword(s):  
Propagation Speed ◽  
Holm Equation ◽  
Infinite Propagation Speed

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

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.

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