Implications of the Lagrange Identity in Thermoelasticity of Dipolar Bodies

2019 ◽  
pp. 291-308
Author(s):  
Marin Marin ◽  
Andreas Öchsner ◽  
Sorin Vlase
Keyword(s):  
Lagrange Identity ◽  
Dipolar Bodies

scholarly journals On Porous Matrices with Three Delay Times: A Study in Linear Thermoelasticity

Mathematics ◽  
2020 ◽  
Vol 8 (3) ◽  
pp. 371 ◽  
Author(s):  
Manuela Carini ◽  
Vittorio Zampoli
Keyword(s):  
Thermal Response ◽  
Initial Boundary ◽  
Initial Boundary Value Problem ◽  
Phase Lag ◽  
Differential Heat ◽  
Lagrange Identity ◽  
Delay Times ◽  
Uniqueness Question ◽  
Linear Thermoelasticity ◽  
Initial Boundary Value

Through the present work, we want to lay the foundation of the well-posedness question for a linear model of thermoelasticity here proposed, in which the presence of voids into the elastic matrix is taken into account following the Cowin–Nunziato theory, and whose thermal response obeys a three-phase lag time-differential heat transfer law. By virtue of the linearity of the model investigated, the basic initial-boundary value problem is conveniently modified into an auxiliary one; attention is paid to the uniqueness question, which is addressed through two alternative paths, i.e., the Lagrange identity and the logarithmic convexity methods, as well as to the continuous dependence issue. The results are achieved under very weak assumptions involving constitutive coefficients and delay times, at most coincident with those able to guarantee the thermodynamic consistency of the model.

On the possibility of locating in time of solutions for thermoelastic porous dipolar bodies

2015 ◽  
Vol 226 (6) ◽  
pp. 2053-2063 ◽  
Author(s):  
Marin Marin ◽  
Ravi P. Agarwal
Keyword(s):  
Dipolar Bodies

scholarly journals A domain of influence in the Moore–Gibson–Thompson theory of dipolar bodies

2020 ◽  
Vol 14 (1) ◽  
pp. 653-660 ◽  
Author(s):  
M. Marin ◽  
M. I. A. Othman ◽  
A. R. Seadawy ◽  
C. Carstea
Keyword(s):  
Dipolar Bodies

scholarly journals Evolution of solutions for dipolar bodies in Thermoelasticity without energy dissipation

2016 ◽  
Vol 24 (1) ◽  
pp. 57-82
Author(s):  
Marin Marin ◽  
Ibrahim Abbas
Keyword(s):  
Energy Dissipation ◽  
A Priori ◽  
A Priori Estimate ◽  
Critical Value ◽  
Spatial Evolution ◽  
Spatial Decay ◽  
Priori Estimate ◽  
Dipolar Bodies ◽  
Growth Properties ◽  
Without Energy Dissipation

AbstractThe aim of our paper is the study of the spatial evolution of vibrations in the context of Thermoelasticity without energy dissipation for dipolar bodies. Once we get an a priori estimate for the amplitude of the vibration, which are assumed being harmonic in time, it is possible to predict some spatial decay or growth properties for the amplitude, provided the frequency of vibration is greater than a certain critical value.

83.67 A Simple Proof of the Lagrange Identity on Vector Products

1999 ◽  
Vol 83 (498) ◽  
pp. 509
Author(s):  
Manuel Alvarez ◽  
Joaquin M. Gutierrez
Keyword(s):  
Simple Proof ◽  
Lagrange Identity

scholarly journals On vibrations in Green-Naghdi thermoelasticity of dipolar bodies

2019 ◽  
Vol 27 (1) ◽  
pp. 125-140 ◽  
Author(s):  
M. Marin ◽  
A. Chirilă ◽  
L. Codarcea ◽  
S. Vlase
Keyword(s):  
Boundary Value Problem ◽  
Boundary Value ◽  
Critical Value ◽  
Spatial Behavior ◽  
Type Iii ◽  
Dipolar Bodies ◽  
Dipolar Structure

Abstract This study is concerned with the theory of thermoelasticity of type III proposed by Green and Naghdi, which is extended to cover the bodies with dipolar structure. In this context we construct a boundary value problem for a prismatic bar which is subjected to some harmonic in time vibrations. For the oscillations whose amplitudes have the frequency lower than a critical value, we deduce some estimates for describing the spatial behavior.

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