Convergence Results for the Double-Diffusion Perturbation Equations

Shi, Jincheng; Luo, Shiguang

doi:10.3390/sym14010067

Cited by 2 publications

(1 citation statement)

References 44 publications

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“…In this section, similar to [18,36], we study double-diffusive convection by considering a porous medium that fills the three-dimensional region and is governed by the following Forchheimer equations:…”

Section: Governing Equationsmentioning

confidence: 99%

A Study of Continuous Dependence and Symmetric Properties of Double Diffusive Convection: Forchheimer Model

et al. 2022

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In this recent work, the continuous dependence of double diffusive convection was studied theoretically in a porous medium of the Forchheimer model along with a variable viscosity. The analysis depicts that the density of saturating fluid under consideration shows a linear relationship with its concentration and a cubic dependence on the temperature. In this model, the equations for convection fluid motion were examined when viscosity changed with temperature linearly. This problem allowed the possibility of resonance between internal layers in thermal convection. Furthermore, we investigated the continuous dependence of this solution based on the changes in viscosity. Throughout the paper, we found an “a priori estimate” with coefficients that relied only on initial values, boundary data, and the geometry of the problem that demonstrated the continuous dependence of the solution on changes in the viscosity, which also helped us to state the relationship between the continuous dependence of the solution and the changes in viscosity. Moreover, we deduced a convergence result based on the Forchheimer model at the stage when the variable viscosity trends toward a constant value by assuming a couple of solutions to the boundary-initial-value problems and defining a difference solution of variables that satisfy a given boundary-initial-value problem.

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Section: Governing Equationsmentioning

confidence: 99%

A Study of Continuous Dependence and Symmetric Properties of Double Diffusive Convection: Forchheimer Model

et al. 2022

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Spatial decay bound and structural stability for the double-diffusion perturbation equations

Li¹,

Chen

2022

MBE

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<abstract><p>In this paper, we study the double-diffusion perturbation equations when the flow is through a porous medium. If the initial conditions satisfy some constraint conditions, the Saint-Venant type spatial decay of solutions for double-diffusion perturbation equations is obtained. Based on the spatial decay bound, the structural stability for the double-diffusion perturbation equations is also established.</p></abstract>

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Convergence Results for the Double-Diffusion Perturbation Equations

Cited by 2 publications

References 44 publications

A Study of Continuous Dependence and Symmetric Properties of Double Diffusive Convection: Forchheimer Model

A Study of Continuous Dependence and Symmetric Properties of Double Diffusive Convection: Forchheimer Model

Spatial decay bound and structural stability for the double-diffusion perturbation equations

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