Abstract The structural stability of the Darcy equations in a bounded region in?R3 was studied.The Robin boundary condition for the temperature T?was imposed.With the aid of some useful priori bounds,we were able to demonstrate the continuous dependence and convergence results for the solution on Robin boundary coefficient k?.
SHI Jincheng, LI Yuanfei. Structural stability of solutions for the Darcy equations in porous medium. Journal of Zhejiang University (Science Edition), 2021, 48(3): 298-303.
1 AMES K A，STRAUGHAN B.Non-Standard and Improperly Posed Problems［M］.San Diego：Academic Press，1997. DOI：10.1016/s0076-5392（97）80007-0 2 NIELD D A，BEJIAN A.Convection in Porous Media［M］. New York：Springer，1992. DOI：10.1007/978-1-4757-2175-1 3 STRAUGHAN B. Stability and Wave Motion in Porous Media［M］. New York：Springer，2008. DOI：10.1007/978-0-387-76543-3_2 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（2）：864-875. DOI： 10.1016/j.jmaa. 2006.08.013 5 FRANCHI F，STRAUGHAN B.Continuous dependence and decay for the Forchheimer equations［J］.Proceedings of the Royal Society A：Mathematical and Physical Sciences，2003，459（2040）：3195-3202. DOI：10.1098/rspa.2003.1169 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 and Physical Sciences，1998，454（1974）：1691-1698. DOI：10.1098/rspa.1998.0227 7 LIN C H，PAYNE L E.Structural stability for a Brinkman fluid［J］.Mathematical Methods in the Applied Sciences，2007，30（5）：567-578. DOI：10. 1002/mma.799 8 CHEN W H，LIU Y.Structural stability for a Brinkman-Forchheimer type model with temperature dependent solubility［J］. Boundary Value Problems，2016，2016（1）：55. 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. DOI：10.1016/j.amc.2014.12.047 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. DOI：10.1016/s0252-9602（16）30128-x 11 WU H L，REN Y，HU F.Continuous dependence property of BSDE with constraints［J］.Applied Mathematics Letters，2015，45：41-46. DOI：10.1016/j.aml.2015.01.002 12 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. DOI：10.1007/s00023-013-0307-z 13 LI Y F，LIN C H.Continuous dependence for the nonhomogeneous Brinkman-Forchheimer equations in a semi-infinite pipe［J］. Applied Mathematics and Computation，2014，244：201-208. DOI：10.1016/j.amc.2014.06.082 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. DOI：10.1016/j.nonrwa.2018.01.007 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. DOI：10.1016/j.matcom.2018.02.009 16 LIU Y.Continuous dependence for a thermal convection model with temperature dependent solubility［J］.Applied Mathematics and Computation，2017，308：18-30. DOI：10.1016/j.amc. 2017.03.004 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 Y F.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. 18 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. LI Y F.Continuous dependence on the viscosity coefficient for the primitive equations［J］.Journal of Shandong University（Science Edition），2019，54（12）：1-12. 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 Y F，GUO L H. 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. 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 Y F. Convergence results on heat source for 2D viscous primitive equations of ocean dynamics［J］.Applied Mathematics and Mechanics，2020，41（3）：339-352. 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. DOI：10.1016/j.nonrwa.2014.07.012 22 WEATHERBURN C E.Differential Geometry of Three Dimensions［M］. Cambridge：Cambridge University Press，1980. 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. DOI：10.1016/j.jmaa.2007.11.036
