《山东大学学报(理学版)》 ›› 2021, Vol. 56 ›› Issue (2): 103-110.doi: 10.6040/j.issn.1671-9352.0.2020.141
• • 上一篇
欧阳柏平,李远飞*
OUYANG Bai-ping, LI Yuan-fei*
摘要： 考虑了有界区域内的多孔介质中的溶解度与温度有关的Brinkman-Forchheimer方程组的解的结构稳定性。首先推出温度与溶解度的一些估计,然后构造一个能量表达式,接着推出能量表达式所满足的的微分不等式,最后积分该微分不等式得到了方程组的解对边界系数的连续依赖性结果。
中图分类号:
| [1] CHEN Wenhui, LIU Yan. Structural stability for a Brinkman-Forchheimer type model with temperature dependent solubility[J/OL]. Boundary Value Problems, 2016 [2020-02-01]. https://link.springer.com/content/pdf/10.1186/s13661-016-0558-y.pdf. [2] CIARLETTAM, STRAUGHAN B, TIBULLO V. Structural stability for a thermal convection model with temperature-dependent solubility[J]. Nonlinear Analysis: Real World Applications, 2015, 22(2):34-43. [3] STRAUGHAN B. The energy method, stability and nonlinear convection[M]. New York: Springer, 2004. [4] AMES K A, STRAUGHAN B. Non-standard and improperly posed problems[M]. San Diego: Academic Press, 1997. [5] HIRSCH M W, SMALE S. Differential equations, dynamical systems, and linear algebra[M]. New York: Academic Press, 1974. [6] STRAUGHAN B. Continuous dependence on the heat source in resonant porous penetrative convection[J]. Studies in Applied Mathematics, 2011, 127(3):302-314. [7] SCOTT N L. Continuous dependence on boundary reaction terms in a porous medium of Darcy type[J]. Journal of Mathematical Analysis and Applications, 2013, 399(2):667-675. [8] SCOTT N L, STRAUGHAN B. Continuous dependence on the reaction terms in porous convection with surface reactions[J]. Quarterly of Applied Mathematics, 2013, 71(3):501-508. [9] HARFASH J. Structural stability for two convection models in a reacting fluid with magnetic field effect[J]. Annales Henri Poincaré, 2014, 15(12):2441-2465. [10] LI Yuanfei, LIN Changhao. Continuous dependence for the non-homogeneous Brinkman-Forchheimer equations in a semi-infinite pipe[J]. Applied Mathematics and Computation, 2014, 244(19):201-208. [11] 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(2):34-43. [12] LIU Yan. Continuous dependence for a thermal convection model with temperature dependent solubility[J]. Applied Mathematics and Computation, 2017, 308(17):18-30. [13] 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. [14] 李远飞.原始方程组对黏性系数的连续依赖性[J].山东大学学报(理学版), 2019, 54(12):1-12. LI Yuanfei. Continuous dependence on the viscosity coefficient for the primitive equations[J]. Journal of Shandong University(Natural Science), 2019, 54(12):1-12. [15] 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-Forchheimertype[J]. Applied Mathematics A Journal of Chinese Universities, 2019, 34(3):315-324. [16] CICHON M, STRAUGHAN B, YANTIR A. On continuous dependence of solutions of dynamic equations[J]. Applied Mathematics and Computation, 2015, 252(3):473-483. [17] MA Heping, LIU Bin. Exact controllability and continuous dependence of fractional neutral intergro-differential equations with state dependent delay[J]. Acta Mathematica Scientia(English Series), 2017, 37(1):235-258. [18] WU Helin, REN Yong, HU Feng. Continuous dependence property of BSDE with constraints[J]. Applied Mathematics Letters, 2015, 45(7):41-46. [19] PAYNE L E, STRAUGHAN B. Analysis of the boundary condition at the interface between a viscous fluid and a porous medium and related modeling questions[J]. Journal de Mathématiques Pures et Appliqués, 1998, 77(4):317-354. [20] LIU Yan, XIAO Shengzhong. Structural stability for the Brinkman fluid interfacing with a Darcy fluid in an unbounded domain[J]. Nonlinear Analysis: Real World Applications, 2018, 42(4):308-333. [21] LIU Yan, XIAO Shengzhong, LIN Yiwu. Continuous dependence for the Brinkman-Forchheimer fluid interfacing with a Darcy fluid in a bounded domain[J]. Mathematics and Computers in Simulation, 2018, 150(8):66-82. [22] 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 the heat source for the 2D viscous primitive equations in ocean dynamics[J]. Applied Mathematics and Mechanics, 2020, 41(3):339-352. [23] LIN C H, 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. |
| [1] | 李远飞. 原始方程组对黏性系数的连续依赖性[J]. 《山东大学学报(理学版)》, 2019, 54(12): 12-23. |
| [2] | 于金彪,任永强,曹伟东,鲁统超,程爱杰,戴涛. 可压多孔介质流的扩展混合元解法[J]. 山东大学学报（理学版）, 2017, 52(8): 25-34. |
| [3] | 李凤萍, 陈光霞. 磁微极流体方程组弱解的正则准则[J]. 山东大学学报（理学版）, 2015, 50(05): 60-67. |
| [4] | 邓利华,尚海锋. 具强非线性源的多孔介质方程的Cauchy 问题[J]. J4, 2012, 47(8): 50-54. |
| [5] | 宋丹丹,原保全*. 可压缩磁流体方程组的显式爆破解[J]. J4, 2012, 47(2): 26-30. |
| [6] | 边东芬，原保全*. 可压缩磁流体方程组整体弱解的不存在性[J]. J4, 2011, 46(4): 42-48. |
| [7] | 佐春梅,程爱杰*. 多孔介质中控制释放耦合问题的有限元方法[J]. J4, 2009, 44(2): 33-38. |
| [8] | 王凤雨. 随机一般多孔介质与快速扩散方程 [J]. J4, 2009, 44(10): 1-13. |
| [9] | 王凤雨. 随机一般多孔介质与快速扩散方程[J]. J4, 2009, 44(10): 1-3. |
| [10] | 肖 华 . 多维反射倒向随机微分方程的解对参数的连续依赖性[J]. J4, 2007, 42(2): 68-71 . |
| [11] | 程爱杰,杜 宁 . 多孔介质中控制释放问题的Galerkin方法[J]. J4, 2006, 41(1): 16-20 . |
|
||
