scholarly journals Convergence rates to the damped system of compressible adiabatic flow through porous media with boundary effect

2019 ◽  
Vol 2019 (1) ◽  
Author(s):  
Lina Zhang ◽  
Shifeng Geng ◽  
Yuling Gao
Keyword(s):  
Porous Media ◽  
Convergence Rates ◽  
Boundary Effect ◽  
Energy Estimates ◽  
Flow Through Porous Media ◽  
Adiabatic Flow ◽  
Weighted Energy ◽  
Damped System ◽  
Weighted Energy Estimates ◽  
Flow Through

AbstractIn this paper, we consider convergence rates to solutions for the damped system of compressible adiabatic flow through porous media with boundary effect. Compared with the results obtained by Pan, the better convergence rates are obtained in this paper. Our approach is based on the technical time-weighted energy estimates.

Asymptotics toward the diffusion wave for a one-dimensional compressible flow through porous media

2003 ◽  
Vol 133 (1) ◽  
pp. 177-196 ◽  
Author(s):  
Kenji Nishihara
Keyword(s):  
Porous Media ◽  
Convergence Rate ◽  
Compressible Flow ◽  
Convergence Rates ◽  
Flow Through Porous Media ◽  
Optimal Convergence Rate ◽  
Diffusion Wave ◽  
One Dimensional ◽  
Optimal Convergence ◽  
Flow Through

Consider the Cauchy problem for a one-dimensional compressible flow through porous media, Hsiao and Liu showed that the solution (υ, u) behaves as the diffusion wave (ῡ, ū), i.e. the solution of the porous-media equation due to the Darcy law. The optimal convergence rates have been obtained by Nishihara and co-workers. When υ0(x) has the same constant state at x = ±∞, the convergence rate ‖(υ − ῡ)(·,t)‖L∞ = O(t−1) obtained is ‘optimal’, since ‖ῡ(·,t)‖∞ = O(t−1/2). However, this ‘optimal’ convergence rate is less sufficient to determine the location of the diffusion wave. Our aim in this paper is to obtain the ‘truly optimal’ convergence rate by choosing suitably located diffusion waves.

Sign in / Sign up

Export Citation Format

Share Document