Well-posedness and decay property for the Cauchy problem of the standard linear solid model with thermoelasticity of type III

被引：6
|
作者：
Wang, Danhua [1 ,4 ]
Liu, Wenjun [1 ,2 ,3 ]
Chen, Kewang [1 ,2 ,3 ]
机构：
[1] Nanjing Univ Informat Sci & Technol, Sch Math & Stat, Nanjing 210044, Peoples R China
[2] Nanjing Univ Informat Sci & Technol, Ctr Appl Math Jiangsu Prov, Nanjing 210044, Peoples R China
[3] Nanjing Univ Informat Sci & Technol, Jiangsu Int Joint Lab Syst Modeling & Data Anal, Nanjing 210044, Peoples R China
[4] Nanjing Xiaozhuang Univ, Coll Informat Engn, Nanjing 211171, Peoples R China
来源：
ZEITSCHRIFT FUR ANGEWANDTE MATHEMATIK UND PHYSIK | 2023年 / 74卷 / 02期
关键词：
Well-posedness; The standard linear solid model; Thermoelasticity type III; Decay estimate; GIBSON-THOMPSON EQUATION; REGULARITY-LOSS TYPE; TIMOSHENKO SYSTEM; GENERAL DECAY; ASYMPTOTIC-BEHAVIOR; MEMORY; VIBRATIONS; RATES;
D O I：
10.1007/s00033-023-01964-4
中图分类号：
O29 [应用数学];
学科分类号：
070104 ;
摘要：
In this paper, we investigate the Cauchy problem related to the standard linear solid model with thermoelasticity of type III in the whole space. By using semigroup theory, we first establish the well-posedness result under certain assumptions on the parameters. By applying the energy method in the Fourier space, we then prove the optimal decay estimate results for both the non-critical and critical cases. Specifically, the decay property of the system is not of the regularity-loss type. In addition, we study the asymptotic expansion of the eigenvalues to analyze the optimality of the decay results.
引用
收藏
页数：16
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