留言板

尊敬的读者、作者、审稿人, 关于本刊的投稿、审稿、编辑和出版的任何问题, 您可以本页添加留言。我们将尽快给您答复。谢谢您的支持!

姓名
邮箱
手机号码
标题
留言内容
验证码

多孔介质中的一类双扩散扰动模型的解的连续依赖性

石金诚 肖胜中

石金诚, 肖胜中. 多孔介质中的一类双扩散扰动模型的解的连续依赖性[J]. 应用数学和力学, 2020, 41(10): 1092-1102. doi: 10.21656/1000-0887.410128
引用本文: 石金诚, 肖胜中. 多孔介质中的一类双扩散扰动模型的解的连续依赖性[J]. 应用数学和力学, 2020, 41(10): 1092-1102. doi: 10.21656/1000-0887.410128
SHI Jincheng, XIAO Shengzhong. Continuous Dependence of Solutions to a Class of Double Diffusion Perturbation Models for Porous Media[J]. Applied Mathematics and Mechanics, 2020, 41(10): 1092-1102. doi: 10.21656/1000-0887.410128
Citation: SHI Jincheng, XIAO Shengzhong. Continuous Dependence of Solutions to a Class of Double Diffusion Perturbation Models for Porous Media[J]. Applied Mathematics and Mechanics, 2020, 41(10): 1092-1102. doi: 10.21656/1000-0887.410128

多孔介质中的一类双扩散扰动模型的解的连续依赖性

doi: 10.21656/1000-0887.410128
基金项目: 国家自然科学基金(11371175)
详细信息
    作者简介:

    石金诚(1983—),男,讲师,硕士(E-mail: hning0818@163.com);肖胜中(1965—),男,教授(通讯作者. E-mail: 1246683963@qq.com).

  • 中图分类号: O175.29

Continuous Dependence of Solutions to a Class of Double Diffusion Perturbation Models for Porous Media

Funds: The National Natural Science Foundation of China(11371175)
  • 摘要: 研究了定义在有界区域上的多孔介质中一类双扩散扰动模型解的结构稳定性。假设模型在区域的边界上满足非齐次Robin边界条件,利用能量分析的方法和微分不等式技术,首先得到了解的先验估计;然后在此基础上推出了关于解的微分不等式;通过积分该微分不等式, 最后建立了解对Lewis数Le的连续依赖性结果。该结果表明,双扩散扰动模型用来描述多孔介质中流体的流动情况是精确的.
  • [1] AMES K A, STRAUGHAN B. Non-Standard and Improperly Pose Problems [M]. San Diego: Academic Press, 1997.
    [2] NIELD D A, BEJAN A. Convection in Porous Media [M]. New York: Springer, 1992.
    [3] STRAUGHAN B. Stability and Wave Motion in Porous Media [M]. New York: Springer, 2008.
    [4] PAYNE L E, SONG J C. Spatial decay in a double diffusive convection problem in Darcy flow[J]. Journal of Mathematical Analysis and Applications,2007,330: 864-875.
    [5] FRANCHI F, STRAUGHAN B. Continuous dependence and decay for the Forchheimer equations[J]. Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences,2003,459: 3195-3202.
    [6] PAYNE L E, STRAUGHAN B. Structural stability for the Darcy equations of flow in porous media[J]. Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences,1998,454: 1691-1698.
    [7] LIN C, PAYNE L E. Structural stability for a Brinkman fluid[J]. Mathematical Methods in the Applied Sciences,2007,30: 567-578.
    [8] CHEN W H, LIU Y. Structural stability for a Brinkman-Forchheimer type model with temperature dependent solubility[J]. Boundary Value Problems,2016,2016. DOI: 10.1186/s13661-016-0558-y.
    [9] CICHON M, STRAUGHAN B, YANTIR A. On continuous dependence of solutions of dynamic equations[J]. Applied Mathematics and Computation,2015,252: 473-483.
    [10] MA H P, LIU B. Exact controllability and continuous dependence of fractional neutral integro-differential equations with state-dependent delay[J]. Acta Mathematica Scientia(English Series),2017,37(1): 235-258.
    [11] WU H L, REN Y, HU F. Continuous dependence property of BSDE with constraints[J]. Applied Mathematics Letters,2015,45: 41-46.
    [12] HARFASH A J. Structural stability for two convection models in a reacting fluid with magnetic field effect[J]. Annales Henri Poincaré,2014,15:2441-2465.
    [13] LI Y, LIN C. Continuous dependence for the nonhomogeneous Brinkman-Forchheimer equations in a semi-infinite pipe[J]. Applied Mathematics and Computation,2014,244: 201-208.
    [14] LIU Y, XIAO S Z. Structural stability for the Brinkman fluid interfacing with a Darcy fluid in an unbounded domain[J]. Nonlinear Analysis: Real World Applications,2018,42: 308-333.
    [15] LIU Y, XIAO S Z, LIN Y W. Continuous dependence for the Brinkman-Forchheimer fluid interfacing with a Darcy fluid in a bounded domain[J]. Mathematics and Computers in Simulation,2018,150: 66-82.
    [16] LIU Y. Continuous dependence for a thermal convection model with temperature dependent solubility[J]. Applied Mathematics and Computation,2017,308: 18-30.
    [17] 李远飞. 大尺度海洋大气动力学三维黏性原始方程对边界参数的连续依赖性[J]. 吉林大学学报(理学版), 2019,57(5): 1053-1059.(LI Yuanfei. Continuous dependence on boundary parameters for three-dimensional viscous primitive equation of large scale ocean atmospheric dynamics[J]. Journal of Jilin University(Science Edition),2019,57(5): 1053-1059.(in Chinese))
    [18] 李远飞. 原始方程组对粘性系数的连续依赖性[J]. 山东大学学报(理学版), 2019,54(12): 12-23.(LI Yuanfei. Continuous dependence on the viscosity coefficient for the primitive equations[J]. Journal of Shandong University( Science Edition), 2019,54(12): 12-23.(in Chinese))
    [19] 李远飞, 郭连红. 具有边界反应Brinkman-Forchheimer型多孔介质的结构稳定性[J]. 高校应用数学学报, 2019,34(3): 315-324.(LI Yuanfei, GUO Lianhong. Structural stability on boundary reaction terms in a porous medium of Brinkman-Forchheimer type[J]. Applied Mathematics: a Journal of Chinese Universities, 2019,34(3): 315-324.(in Chinese))
    [20] 李远飞. 海洋动力学中二维黏性原始方程组解对热源的收敛性[J]. 应用数学和力学, 2020,41(3): 339-352.(LI Yuanfei. Convergence results on heat source for 2D viscous primitive equations of ocean dynamics[J]. Applied Mathematics and Mechanics,2020,41(3): 339-352.(in Chinese))
    [21] CIARLETTA M, STRAUGHAN B, TIBULLO V. Structural stability for a thermal convection model with temperature dependent solubility[J]. Nonlinear Analysis: Real World Applications,2015,22: 34-43.
    [22] STRAUGHAN B. Anisotropic inertia effect in microfluidic porous thermosolutal convection[J]. Microfluidics and Nanofluidics,2014,16: 361-368.
    [23] 王双明. 一类具有时滞的周期流行病模型的动力学分析[J]. 山东大学学报(理学版), 2017,52(1): 81-87.(WANG Shuangming. Dynamical analysis of a class of periodic epidemic model with delay[J]. Journal of Shandong University (Natural Science),2017,52(1): 81-87.(in Chinese))
    [24] WEATHERBURN C E. Differential Geometry of Three Dimensions [M]. London: Cambridge University Press, 1980.
    [25] LIN C, PAYNE L E. Continuous dependence on the Soret coefficient for double diffusive convection in Darcy flow[J]. Journal of Mathematical Analysis and Applications,2008,342(1): 311-325.
  • 加载中
计量
  • 文章访问数:  485
  • HTML全文浏览量:  74
  • PDF下载量:  359
  • 被引次数: 0
出版历程
  • 收稿日期:  2020-05-08
  • 修回日期:  2020-06-09
  • 刊出日期:  2020-10-01

目录

    /

    返回文章
    返回