scholarly journals Nonlinear thermoelastic plate equations – Global existence and decay rates for the Cauchy problem

2017 ◽  
Vol 263 (12) ◽  
pp. 8138-8177 ◽  
Author(s):  
Reinhard Racke ◽  
Yoshihiro Ueda
Keyword(s):  
Cauchy Problem ◽  
Global Existence ◽  
Decay Rates ◽  
The Cauchy Problem ◽  
Plate Equations ◽  
Thermoelastic Plate

scholarly journals Decay properties for evolution-parabolic coupled systems related to thermoelastic plate equations

2021 ◽  
Vol 7 (1) ◽  
pp. 260-275
Author(s):  
Zihan Cai ◽  
◽  
Yan Liu ◽  
Baiping Ouyang ◽  
Keyword(s):  
Cauchy Problem ◽  
Phase Space ◽  
Coupled Systems ◽  
Decay Properties ◽  
Representation Of Solutions ◽  
The Cauchy Problem ◽  
Plate Equations ◽  
Thermoelastic Plate ◽  
Local Operators ◽  
Non Local

<abstract><p>In this paper, we consider the Cauchy problem for a family of evolution-parabolic coupled systems, which are related to the classical thermoelastic plate equations containing non-local operators. By using diagonalization procedure and WKB analysis, we derive representation of solutions in the phase space. Then, sharp decay properties in a framework of $ L^p-L^q $ are investigated via these representations. Particularly, some thresholds for the regularity-loss type decay properties are found.</p></abstract>

scholarly journals Decay properties for evolution-parabolic coupled systems related to thermoelastic plate equations

2021 ◽  
Author(s):  
Yan Liu ◽  
Zihan Cai ◽  
Shuanghu Zhang
Keyword(s):  
Cauchy Problem ◽  
Phase Space ◽  
Coupled Systems ◽  
Decay Properties ◽  
Representation Of Solutions ◽  
The Cauchy Problem ◽  
Plate Equations ◽  
Thermoelastic Plate ◽  
Local Operators ◽  
Non Local

In this paper, we consider the Cauchy problem for a family of evolution-parabolic coupled systems, which are related to the classical thermoelastic plate equations containing non-local operators. By using diagonalization procedure and WKB analysis, we derive representation of solutions in the phase space. Then, sharp decay properties in a framework of $L^p-L^q$ are investigated via these representations. Particularly, some thresholds for the regularity-loss type decay properties are found.

scholarly journals Global existence of solution for multidimensional generalized double dispersion equation

2019 ◽  
Vol 2019 (1) ◽  
Author(s):  
Xiaoqiang Dai
Keyword(s):  
Cauchy Problem ◽  
Global Existence ◽  
Dispersion Equation ◽  
Existence Of Solutions ◽  
Existence Of Solution ◽  
New Methods ◽  
Global Existence Of Solutions ◽  
The Cauchy Problem ◽  
Double Dispersion

Abstract In this paper, we study the Cauchy problem of multidimensional generalized double dispersion equation. To prove the global existence of solutions, we introduce some new methods and ideas, and fill some gaps in the established results.

scholarly journals Global existence of strong solutions for incompressible hydrodynamic flow of liquid crystals with vacuum

Filomat ◽  
2013 ◽  
Vol 27 (7) ◽  
pp. 1247-1257 ◽  
Author(s):  
Shijin Ding ◽  
Jinrui Huang ◽  
Fengguang Xia
Keyword(s):  
Cauchy Problem ◽  
Liquid Crystals ◽  
Global Existence ◽  
Existence And Uniqueness ◽  
Strong Solutions ◽  
Hydrodynamic Flow ◽  
Three Dimensions ◽  
Small Initial Data ◽  
The Cauchy Problem ◽  
Global Existence And Uniqueness

We consider the Cauchy problem for incompressible hydrodynamic flow of nematic liquid crystals in three dimensions. We prove the global existence and uniqueness of the strong solutions with nonnegative p0 and small initial data.

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