温度相关双扩散模型在半无穷柱体上的结构稳定性

Acta mathematica scientia,Series A ›› 2024, Vol. 44 ›› Issue (1): 120-132.

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Structural Stability of Temperature Dependent Double Diffusion Model on a Semi-infinite Cylinder

Li Yuanfei^*(),Li Dandan,Shi Jincheng

Department of Apllied Mathematics, Guangzhou Huashang College, Guangzhou 511300

Received:2022-11-30 Revised:2023-06-20 Online:2024-02-26 Published:2024-01-10
Supported by:
Research Team Project of Guangzhou Huashang University(2021HSKT01);National Natural Science Foundation of China(11371175)

Abstract

Abstract:

A simplified temperature dependent double diffusion model defined on a semi-infinite cylinder is studied. By using a prior estimates and weighted energy analysis, it is proved that the solution of the model decays exponentially with the space variable when the boundary conditions satisfy certain constraints. The structural stability of the solution to the interaction coefficient is obtained by using the prior bounds and decay result of the solution.

Key words: Double diffusion model, Spatial attenuation, Structural stability, Interaction coefficient

CLC Number:

O175.29

Li Yuanfei, Li Dandan, Shi Jincheng. Structural Stability of Temperature Dependent Double Diffusion Model on a Semi-infinite Cylinder[J].Acta mathematica scientia,Series A, 2024, 44(1): 120-132.

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References

[1]	Nield D A. A note on modelling of local thermal non-equilibrium in a structured porous medium. Int J Heat Mass Transfer, 2002, 45: 4367-4368
[2]	Nield D A. Effects of local thermal non-equilibrium in steady convection processes in saturated porous media: forced convection in a channel. J Porous Media, 1998, 1: 181-186
[3]	Nield D A, Kuznetsov A V. The onset of convection in a bidisperse porous medium. Int J Heat Mass Transfer, 2006, 49: 3068-3074
[4]	Falsaperla P, Mulone G, Straughan B. Bidispersive-inclined convection. Proc R Soc A, 2016, 472: 20160480
[5]	Franchi F, Nibbi R, Straughan B. Continuous dependence on modelling for temperature-dependent bidispersiveflow. Proc R Soc A, 2017, 473(2208): 20170485.
[6]	Li Y F, Lin C H. Continuous dependence for the nonhomogeneous Brinkman-Forchheimer equations in a semi-infinite pipe. Applied Mathematics and Computation, 2014, 244: 201-208
[7]	李远飞, 李志青. 具有非线性边界条件的瞬态热传导方程的二择一结果. 数学物理学报, 2020, 40A(5): 1248-1258
[7]	Li Y F, Li Z Q. Phragmén-Lindel?f Type Results for transient heat conduction equation with nonlinear boundary conditions. Acta Mathematica Scientia, 2020, 40A(5): 1248-1258
[8]	Scott N L. Continuous dependence on boundary reaction terms in a porous medium of Darcy type. J Math Anal Appl, 2013, 399: 667-675
[9]	李远飞, 肖胜中, 曾鹏. 饱和蒸汽大气原始方程组的连续依赖性. 华东师范大学学报 (自然科学版), 2021, 2021(3): 34-46
[9]	Li Y F, Xiao S Z, Zeng P. Continuous dependence of primitive equations of the atmosphere with vapor saturation. Journal of East China Normal University (Natural Science), 2021, 2021(3): 34-46
[10]	Liu Y. Continuous dependence for a thermal convection model with temperature-dependent solubility. Applied Mathematics and Computation, 2017, 3008: 18-30
[11]	Liu Y, Du Y, Lin C H. Convergence and continuous dependence results for the Brinkman equations. Applied Mathematics and Computation, 2010, 215:, 4443-4455
[12]	Ciarletta M, Straughan B, Tibullo V. Structural stability for a thermal convection model with temperature-dependent solubility. Nonlinear Analysis Real World Applications, 2015, 22: 34-43
[13]	Payne L E, Song J C. Spatial decay estimates for the Brinkman and Darcy flows in a semi-infinite cylinder. Continuum Mech Thermodyn, 1997, 9: 175-190
[14]	李远飞. Keller-Segel 趋化模型解的全局存在性和爆破时间的下界估计. 应用数学和力学, 2022, 43(7): 816-824
[14]	Li Y F. Global existence of solutions and lower bound estimate of blow-up time for the Keller-Segel chemotaxis model. Applied Mathematics and Mechanics, 2022, 43(7): 816-824
[15]	Payne L E, Song J C. Spatial decay bounds for double diffusive convection in Brinkman flow. Journal of Differential Equations, 2008, 244: 413-430
[16]	Horgan C O, Wheeler L T. Spatial decay estimates for the Navier-Stokes equations with application to the problem of entry flow. SIAM J Appl Math, 1978, 35: 97-116

Structural Stability of Temperature Dependent Double Diffusion Model on a Semi-infinite Cylinder

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