《山东大学学报(理学版)》 ›› 2020, Vol. 55 ›› Issue (12): 1-12.doi: 10.6040/j.issn.1671-9352.0.2020.201
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李远飞,陈雪姣,石金诚
LI Yuan-fei， CHEN Xue-jiao， SHI Jin-cheng
摘要： 考虑定义在一个半无穷柱体上二元混合物中的热传导方程,其中柱体的母线平行于坐标轴。假设方程在柱体的侧面上满足非齐次Neumann边界条件,在柱体的有限端满足非线性条件,运用能量估计的方法,得到了方程的Phragmén-Lindelöf二择性结果。在衰减的情形下,为了使结果有意义,建立全能量的上界。
中图分类号:
| [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. |
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