We consider the system of equations determining the linear thermoelastic deformations of dielectrics within the recently called Moore-Gibson-Thompson(MGT)theory.First,we obtain the system of equations for such a case....We consider the system of equations determining the linear thermoelastic deformations of dielectrics within the recently called Moore-Gibson-Thompson(MGT)theory.First,we obtain the system of equations for such a case.Second,we consider the case of a rigid solid and show the existence and the exponential decay of solutions.Third,we consider the thermoelastic case and obtain the existence and the stability of the solutions.Exponential decay of solutions in the one-dimensional case is also recalled.展开更多
In this paper,the authors consider the inverse problem for the Moore-Gibson-Thompson equation with a memory term and variable diffusivity,which introduce a sort of delay in the dynamics,producing nonlocal effects in t...In this paper,the authors consider the inverse problem for the Moore-Gibson-Thompson equation with a memory term and variable diffusivity,which introduce a sort of delay in the dynamics,producing nonlocal effects in time.The H¨older stability of simultaneously determining the spatially varying viscosity coefficient and the source term is obtained by means of the key pointwise Carleman estimate for the Moore-Gibson-Thompson equation.For the sake of generality in mathematical tools,the analysis of this paper is discussed within the framework of Riemannian geometry.展开更多
In this article,the Moore-Gibson-Thompson heat equation in three-dimensional cylindrical domain are studied.Using a second order differential inequality,we obtain that the solution can decay exponentially as the dista...In this article,the Moore-Gibson-Thompson heat equation in three-dimensional cylindrical domain are studied.Using a second order differential inequality,we obtain that the solution can decay exponentially as the distance from the entry section tends to infinity.Our result can be seen as a version of Saint-Venant principle.展开更多
The present study enlightens the two-dimensional analysis of the thermo-mechanical response for a mi-cropolar double porous thermoelastic material with voids(MDPTMWV)by virtue of Eringen’s theory of nonlocal elastici...The present study enlightens the two-dimensional analysis of the thermo-mechanical response for a mi-cropolar double porous thermoelastic material with voids(MDPTMWV)by virtue of Eringen’s theory of nonlocal elasticity.Moore-Gibson-Thompson(MGT)heat equation is introduced to the considered model in the context of memory-dependent derivative and variable conductivity.By employing the normal mode technique,the non-dimensional coupled governing equations of motion are solved to determine the an-alytical expressions of the displacements,temperature,void volume fractions,microrotation vector,force stress tensors,and equilibrated stress vectors.Several two-dimensional graphs are presented to demon-strate the influence of various parameters,such as kernel functions,thermal conductivity,and nonlocality.Furthermore,different generalized thermoelasticity theories with variable conductivity are compared to visualize the variations in the distributions associated with the prior mentioned variables.Some particu-lar cases are also discussed in the presence and absence of different parameters.展开更多
This paper is concerned with a third order in time linear Moore-Gibson-Thompson equation which describes the acoustic velocity potential in ultrasound wave program.Influenced by the work of Kaltenbacher,Lasiecka and M...This paper is concerned with a third order in time linear Moore-Gibson-Thompson equation which describes the acoustic velocity potential in ultrasound wave program.Influenced by the work of Kaltenbacher,Lasiecka and Marchand(Control Cybernet.2011,40:971-988),we establish an observability inequality of the conservative problem,and then discuss the equivalence between the exponential stabilization of a dissipative system and the internal observational inequality of the corresponding conservative system.展开更多
文摘We consider the system of equations determining the linear thermoelastic deformations of dielectrics within the recently called Moore-Gibson-Thompson(MGT)theory.First,we obtain the system of equations for such a case.Second,we consider the case of a rigid solid and show the existence and the exponential decay of solutions.Third,we consider the thermoelastic case and obtain the existence and the stability of the solutions.Exponential decay of solutions in the one-dimensional case is also recalled.
基金supported by the National Key R&D Program of China under Grant No.2018YFA0703800the National Science Foundation of China under Grant No.T2293770。
文摘In this paper,the authors consider the inverse problem for the Moore-Gibson-Thompson equation with a memory term and variable diffusivity,which introduce a sort of delay in the dynamics,producing nonlocal effects in time.The H¨older stability of simultaneously determining the spatially varying viscosity coefficient and the source term is obtained by means of the key pointwise Carleman estimate for the Moore-Gibson-Thompson equation.For the sake of generality in mathematical tools,the analysis of this paper is discussed within the framework of Riemannian geometry.
基金Supported by the National Natural Science Foundation of China (11371175)the Research Team of Guangzhou Huashang College(2021HSKT01)Guangzhou Huashang College Mentorship Program(2020HSDS16)。
文摘In this article,the Moore-Gibson-Thompson heat equation in three-dimensional cylindrical domain are studied.Using a second order differential inequality,we obtain that the solution can decay exponentially as the distance from the entry section tends to infinity.Our result can be seen as a version of Saint-Venant principle.
文摘The present study enlightens the two-dimensional analysis of the thermo-mechanical response for a mi-cropolar double porous thermoelastic material with voids(MDPTMWV)by virtue of Eringen’s theory of nonlocal elasticity.Moore-Gibson-Thompson(MGT)heat equation is introduced to the considered model in the context of memory-dependent derivative and variable conductivity.By employing the normal mode technique,the non-dimensional coupled governing equations of motion are solved to determine the an-alytical expressions of the displacements,temperature,void volume fractions,microrotation vector,force stress tensors,and equilibrated stress vectors.Several two-dimensional graphs are presented to demon-strate the influence of various parameters,such as kernel functions,thermal conductivity,and nonlocality.Furthermore,different generalized thermoelasticity theories with variable conductivity are compared to visualize the variations in the distributions associated with the prior mentioned variables.Some particu-lar cases are also discussed in the presence and absence of different parameters.
基金Supported by the National Natural Science Foundation of China(11771216)the Key Research and Development Program of Jiangsu Province(Social Development)(BE2019725)the Qing Lan Project of Jiangsu Province。
文摘This paper is concerned with a third order in time linear Moore-Gibson-Thompson equation which describes the acoustic velocity potential in ultrasound wave program.Influenced by the work of Kaltenbacher,Lasiecka and Marchand(Control Cybernet.2011,40:971-988),we establish an observability inequality of the conservative problem,and then discuss the equivalence between the exponential stabilization of a dissipative system and the internal observational inequality of the corresponding conservative system.
