scholarly journals Spatial decay estimates for the Fochheimer equations interfacing with a Darcy equations

2021 ◽  
Vol 6 (11) ◽  
pp. 12632-12649
Author(s):  
Ze Wang ◽  
◽  
Yan Zhang ◽  
Jincheng Shi ◽  
◽  
...  
Keyword(s):  
Exponential Decay ◽  
Differential Inequality ◽  
Darcy Flow ◽  
Decay Estimates ◽  
Spatial Decay ◽  
First Order ◽  
Darcy Equations

<abstract><p>Spatial decay estimates for the Fochheimer fluid interfacing with a Darcy flow in a semi-infinite pipe was studied. The exponential decay result can be obtained by integrating a first-order differential inequality. The result can be seen as the usage of Saint-Venant's principle for the interfacing fluids.</p></abstract>

scholarly journals Spatial Behavior of a Coupled System of Wave-Plate Type

2014 ◽  
Vol 2014 ◽  
pp. 1-13 ◽  
Author(s):  
Gusheng Tang ◽  
Yan Liu ◽  
Wenhui Liao
Keyword(s):  
Differential Inequality ◽  
Coupled System ◽  
Second Order ◽  
Spatial Behavior ◽  
Decay Estimates ◽  
Spatial Decay ◽  
Area Measure ◽  
First Order ◽  
Wave Plate ◽  
Plate Type

The spatial behavior of a coupled system of wave-plate type is studied. We get the alternative results of Phragmén-Lindelöf type in terms of an area measure of the amplitude in question based on a first-order differential inequality. We also get the spatial decay estimates based on a second-order differential inequality.

scholarly journals Structural stability for the Boussinesq equations interfacing with Darcy equations in a bounded domain

2021 ◽  
Vol 2021 (1) ◽  
Author(s):  
Yuanfei Li ◽  
Shuanghu Zhang ◽  
Changhao Lin
Keyword(s):  
Bounded Domain ◽  
Structural Stability ◽  
Differential Inequality ◽  
Continuous Dependence ◽  
A Priori ◽  
Boussinesq Equations ◽  
Interface Boundary ◽  
A Priori Bounds ◽  
First Order ◽  
Darcy Equations

AbstractA priori bounds were derived for the flow in a bounded domain for the viscous-porous interfacing fluids. We assumed that the viscous fluid was slow in $\Omega _{1}$ Ω 1 , which was governed by the Boussinesq equations. For a porous medium in $\Omega _{2}$ Ω 2 , we supposed that the flow satisfied the Darcy equations. With the aid of these a priori bounds we were able to demonstrate the result of the continuous dependence type for the Boussinesq coefficient λ. Following the method of a first-order differential inequality, we can further obtain the result that the solution depends continuously on the interface boundary coefficient α. These results showed that the structural stability is valid for the interfacing problem.

Spatial Decay Estimates for a Class of Thermoelastic Plates

2021 ◽  
Vol 42 (0) ◽  
pp. 1-9
Author(s):  
SHI Jincheng ◽  
◽  
◽  
XIAO Shengzhong ◽  
◽  
...  
Keyword(s):  
Decay Estimates ◽  
Spatial Decay ◽  
Thermoelastic Plates
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