Spatial Alternative and Stability of Type Ⅲ Thermoelastic Equations

LI Yuanfei; XIAO Shengzhong; CHEN Xuejiao

doi:10.21656/1000-0887.410270

Volume 42 Issue 4

Apr. 2021

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LI Yuanfei, XIAO Shengzhong, CHEN Xuejiao. Spatial Alternative and Stability of Type Ⅲ Thermoelastic Equations[J]. Applied Mathematics and Mechanics, 2021, 42(4): 431-440. doi: 10.21656/1000-0887.410270

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Spatial Alternative and Stability of Type Ⅲ Thermoelastic Equations

doi: 10.21656/1000-0887.410270

¹Department of Applied Mathematics, Huashang College, Guangdong University of Finance & Economics, Guangzhou 511300, P.R.China
²Guangdong AIB Polytechnic, Guangzhou 510507, P.R.China

Received Date: 2020-09-11
Rev Recd Date: 2020-11-25
Publish Date: 2021-04-01

Abstract

Abstract

The spatial alternative of type Ⅲ thermoelastic equations in a semi-infinite region was considered. The equations were assumed to satisfy certain initial and boundary conditions, and the solution was proved to grow exponentially or alternatively decay exponentially respectively, with spatial variables on a semi-infinite cylinder with the energy analysis method. The continuous dependence of solutions on the coefficients of equations was established.
- thermoelastic equation,
- alternative,
- spatial decay,
- structural stability

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References

[1]	GREEN A E, NAGHDI P M. A re-examination of the basic postulates of thermomechanics[J]. Proceedings of the Royal Society A,1991,432(1885): 171-194.
[2]	GREEN A E, NAGHDI P M. On undamped heat waves in an elastic solid[J]. Journal of Thermal Stresses,1992,15: 253-264.
[3]	GREEN A E, NAGHDI P M. Thermoelasticity without energy dissipation[J]. Journal of Elasticity,1993,31: 189-208.
[4]	ZHANG X, ZUAZUA E. Decay of solutions of the system of thermoelasticity of type Ⅲ[J]. Communications in Contemporary Mathematics,2003,5(1): 25-83.
[5]	MESSAOUNDI S A, SOUFYANE A. Boundary stabilization of memory type in thermoelasticity of type Ⅲ[J]. Applicable Analysis,2008, 87(1): 13-28.
[6]	HORGAN C O, PAYNE L E. Phragmén-Lindelf type results for harmonic functions with nonlinear boundary conditions[J]. Archive for Rational Mechanics and Analysis,1993,122(2): 123-144.
[7]	LIN C H. A Phragmén-Lindel-f alternative for a class of second order quasilinear equations in R³[J]. Acta Mathematica Scientia,1996,16(2): 181-191.
[8]	LIU Y, LIN C H. Phragmén-Lindelf type alternative results for the Stokes flow equation[J]. Mathematical Inequalities & Applications,2006,9(4): 671-694.
[9]	LESEDUARTE M C, QUINTANILLA R. Phragmén-Lindelf of alternative for the Laplace equation with dynamic boundary conditions[J]. Journal of Applied Analysis and Computation,2017,7(4): 1323-1335.
[10]	QUINTANILLA R. Some remarks on the fast spatial growth/decay in exterior regions[J]. Zeitschrift für angewandte Mathematik und Physik,2019,70: 83.
[11]	李远飞, 石金诚, 曾鹏. 三维柱体上调和方程的二则一结果[J]. 海南大学学报自然科学版, 2020,38(1): 6-12.(LI Yuanfei, SHI Jincheng, ZENG Peng. Phragmén-Lindelf alternative type results for harmonic equation in a 3D cylinder[J]. Natural Science Journal of Hainan University,2020,38(1): 6-12.(in Chinese))
[12]	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-Lindelf type results for non-standard Stokes flow equations around semi-infinite cylinder[J]. Applied Mathematics and Mechanics,2020,41(4): 406-419.(in Chinese))
[13]	SONG J C, YOON D S. Phragmén-Lindelf type and continuous dependence results in generalized dissipative heat conduction[J]. Journal of the Korean Mathematical Society,1998,35(4): 945-960.
[14]	PAYNE L E, SCHAEFER P W. Some Phragmén-Lindelf type results for the biharmonic equation[J]. Zeitschrift für Angewandte Mathematik und Physik,1994,45(3): 414-432.
[15]	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))
[16]	LIU Y, XIAO S H, LIN C. Continuous dependence for the Brinkman-Forchheimer fluid interfacing with a Darcy fluid in a bounded domain[J]. Mathematics and Computers in Simulation,2018,150: 66-88.
[17]	LIU Y. Continuous dependence for a thermal convection model with temperature-dependent solubility[J]. Applied Mathematics and Computation, 2017,308: 18-30.
[18]	李远飞. 大尺度湿大气原始方程组对黏性系数的连续依赖性[J]. 吉林大学学报(理学版), 2020,58(4): 744-752.(LI Yuanfei. Continuous dependence of primitive equations of large-scale moist atmosphere on viscosity coefficient[J]. Journal of Jilin University (Science Edition),2020,58(4): 744-752.(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,〖STHZ〗 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]	郭连红, 李远飞. 大尺度湿大气原始方程组对边界参数的连续依赖性[J]. 应用数学和力学, 2020,〖STHZ〗 41(9): 1036-1047.(GUO Lianhong, LI Yuanfei. Continuous dependence on boundary on boundary parameters of the original parameters of the original equations for large-scale wet atmosphere[J]. Applied Mathematics and Mechanics,2020,41(9): 1036-1047.(in Chinese))
[21]	KNOPS R J, QUINTANILLA R. Spatial behaviour in thermoelastostatic cylinders of indefinitely increasing cross-section[J]. Journal of Elasticity,2015,121: 89-117.
[22]	KNOPS R J, QUINTANILLA R. Spatial decay in transient heat conduction for general elongated regions[J]. Quarterly of Applied Mathematics,2018,76: 611-625.