《山东大学学报(理学版)》 ›› 2020, Vol. 55 ›› Issue (12): 1-12.

• •

### 二元混合物中的热传导方程Phragmén-Lindelöf二择性

1. 广东财经大学华商学院数据科学学院, 广东 广州 511300
• 发布日期:2020-12-01
• 作者简介:李远飞(1982— ),男,博士,教授,研究方向为偏微分方程. E-mail:liqfd@163.com
• 基金资助:
广东省普通高校重点资助项目(2019KZDXM042)

### Phragmén-Lindelof alternative for the heat conduction equations in a binary mixture

LI Yuan-fei， CHEN Xue-jiao， SHI Jin-cheng

1. School of Data Science, Huashang College Guangdong University of Finance &
Economics, Guangzhou 511300, Guangdong, China
• Published:2020-12-01

Abstract: The heat conduction equations in a binary mixture which are defined in a semi-infinite cylinder is considered and the generatrix of the cylinder is parallel to the coordinate axis. Assuming that the equations satisfy the nonhomogeneous Neumann boundary conditions on the lateral surface of the cylinder and the nonlinear conditions on the finite end of the cylinder, the method of energy estimation is used to obtain the Phragmén-Lindelöf alternative results of the equations. In the case of decay, in order to make the results meaningful, the upper bound of total energy is established.

• O175.29
 [1] HORGAN C O, QUINTANILLA R. Spatial decay of transient end effects for nonstandard linear diffusion problems[J]. IMA Journal of Applied Mathematics, 2005, 70(1):119-128.[2] NAYFEH A H. A continuum mixture theory of heat conduction in laminated composite[J]. Journal of Appllied Mechanics, 1975, 42(2):399-404.[3] IESAN D. A theory of mixtures with different constituent temperatures[J]. Journal of Thermal Stresses, 1997, 20(2):147-167.[4] QUINATANILLA R. Study of the solutions of the propagation of heat in mixtures[J]. Dynamics of Continuous, Discrete and Impulsive Systems Series B: Applications and Algorithms, 2001, 8(1):15-28. [5] IESAN D D, QUINATANILLA R. On the problem of propagation of heat in mixtures[J]. Applied Mechanics and Engineering, 1999, 4(3):529-552.[6] HORGAN C O, PAYNE L E. Phragmén-Lindelöf type results for harmonic functions with nonlinear boundary conditions[J]. Archive for Rational Mechanics and Analysis, 1993, 122(2):123-144.[7] PAYNE L E, SCHAEFER P W. Some Phragmén-Lindelöf type results for the biharmonic equation[J]. Zeitschrift für Angewandte Mathematik und Physik ZAMP, 1994, 45(3):414-432.[8] MARKOWSKY G. The exit time of planar Brownian motion and the Phragmén-Lindelöf principle[J]. Journal of Mathematical Analysis & Applications, 2013, 422(1):638-645.[9] GENTILI G, STOPPATO C, STRUPPA D C. A Phragmén-Lindelöf principle for slice regular functions[J]. Bulletin of the Belgian Mathematical Society-Simon Stevin, 2009, 18(4):749-759.[10] LIU Yan, LIN Changhao. Phragmén-Lindelöf alternative type alternative results for the stokes flow equation[J]. Mathematical Inequalities & Applications, 2006, 9(4):671-694.[11] LESEDUARTE M C, QUINATANILLA R. Phragmén-Lindelöf of alternative for the Laplace equation with dynamic boundary conditions[J]. Journal of Applied Analysis and Computation, 2017, 7(4):1323-1335[12] LIESS Otto. Necessary conditions in Phragmén-Lindelöf type estimates and decomposition of holomorphic functions[J]. Mathematische Nachrichten, 2017, 290(8/9):1328-1346. [13] 李远飞. 在一个半无穷柱体上的非标准Stokes流体方程的二择一问题[J]. 应用数学和力学, 2020,41(4):406-419. LI Yuanfei. Phragmén-Lindelöf type results for non-standard Stokes flow equations around semi-infinite cylinder[J]. Applied Mathematics and Mechanics, 2020, 41(4):406-419.[14] 李远飞, 石金诚, 曾鹏. 三维柱体上调和方程的二择一结果[J]. 海南大学学报(自然科学版), 2020, 38(1):6-12. LI Yuanfei, SHI Jinchen, ZENG Pemg. Phragmén-Lindelöf alternative type results for the harmonic equation in a 3D cylinder[J]. Journal of Hainan University(Natural Science), 2020, 38(1):6-12.[15] JAVIER J G, JAVIER S, GERHARD S. A Phragmén-Lindelöf theorem via proximate orders, and the propagation of asymptotics[J]. The Journal of Geometric Analysis, 2019(5):1-26. [16] TATEYAMA S. The Phragmén-Lindelöf theorem for Lp-viscosity solutions of fully nonlinear parabolic equations with unbounded ingredients[J]. Journal of Mathematical Pures and Applications, 2020, 133:172-184.[17] 李远飞.海洋动力学中二维粘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.[18] 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 Application., 2008, 342(1):311-325.[19] YANG Xin, ZHOU Zhengfang. Blow-up problems for the heat equation with a local nonlinear Neumann boundary condition[J]. Journal of Differential Equations, 2016, 261(5):2738-2783.
 [1] 宗西举,王中华. 一维黏性Camassa-Holm方程描述的液体-固体的相互作用[J]. J4, 2011, 46(2): 34-38.
Viewed
Full text

Abstract

Cited

Shared
Discussed