Semi-analytical solutions to one-dimensional advection–diffusion equations with variable diffusion coefficient and variable flow velocity

2013 ◽  
Vol 221 ◽  
pp. 268-281 ◽  
Author(s):  
Xinfeng Jia ◽  
Fanhua Zeng ◽  
Yongan Gu
Keyword(s):  
Diffusion Coefficient ◽  
Flow Velocity ◽  
Analytical Solutions ◽  
Diffusion Equations ◽  
Variable Flow ◽  
One Dimensional ◽  
Variable Diffusion Coefficient ◽  
Advection Diffusion ◽  
Variable Diffusion

Analytical solutions of the space–time fractional Telegraph and advection–diffusion equations

2018 ◽  
Vol 491 ◽  
pp. 810-819 ◽  
Author(s):  
Ashraf M. Tawfik ◽  
Horst Fichtner ◽  
Reinhard Schlickeiser ◽  
A. Elhanbaly
Keyword(s):  
Analytical Solutions ◽  
Space Time ◽  
Diffusion Equations ◽  
Advection Diffusion

scholarly journals Role of Time Relaxation in a One-Dimensional Diffusion-Advection Model of Water and Salt Transport

2015 ◽  
Vol 2015 ◽  
pp. 1-6 ◽  
Author(s):  
Igor Medved’ ◽  
Robert Černý
Keyword(s):  
Diffusion Coefficient ◽  
Structural Damage ◽  
Building Materials ◽  
Chloride Transport ◽  
Salt Transport ◽  
One Dimensional ◽  
Advection Diffusion ◽  
Dimensional Diffusion ◽  
Lime Plaster

The transport of salt, necessarily coupled with the transport of water, through porous building materials may heavily limit their durability due to possible deterioration and structural damage. Usually, the binding of salt to the pore walls is assumed to occur instantly, as soon as the salt is transported by water to a given position. We consider the advection-diffusion model of the transport and generalize it to include possible delays in the binding. Applying the Boltzmann-Matano method, we calculate the diffusion coefficient of the salt in dependence on the salt concentration and show that it increases with the rate of binding. We apply our results to an example of the chloride transport in a lime plaster.

scholarly journals General Asymptotic Supnorm Estimates for Solutions of One-Dimensional Advection-Diffusion Equations in Heterogeneous Media

2014 ◽  
Vol 2014 ◽  
pp. 1-8 ◽  
Author(s):  
José A. Barrionuevo ◽  
Lucas S. Oliveira ◽  
Paulo R. Zingano
Keyword(s):  
Initial Data ◽  
Large Time ◽  
Heterogeneous Media ◽  
Diffusion Equations ◽  
Open Problems ◽  
New Techniques ◽  
One Dimensional ◽  
Advection Diffusion

We derive general bounds for the large time size of supnorm values ∥u(·,t)∥L∞(ℝ) of solutions to one-dimensional advection-diffusion equations ut+(b(x,t)u)x=uxx,x∈ℝ,t>0 with initial data u(·,0)∈Lp0(ℝ)∩L∞(ℝ) for some 1≤p0<∞ and arbitrary bounded advection speeds b(x,t), introducing new techniques based on suitable energy arguments. Some open problems and related results are also given.

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