Lagrange Identity for Polynomials and δ-Codes of Lengths 7t and 13t

1983 ◽  
Vol 88 (4) ◽  
pp. 746 ◽  
Author(s):  
C. H. Yang
Keyword(s):  
Lagrange Identity

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.

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 An approach with Lagrange identity of the mixed problem in theory of strain gradient thermoelasticity

2020 ◽  
Vol 34 ◽  
pp. 01004
Author(s):  
Marin Marin
Keyword(s):  
Mixed Problem ◽  
Strain Gradient ◽  
Continuous Dependence ◽  
Initial Boundary ◽  
Boundary Values ◽  
Conservation Of Energy ◽  
Lagrange Identity ◽  
Uniqueness Of The Solution ◽  
Continuous Dependence Of Solutions ◽  
Elastic Coefficients

In our paper we first define the mixed initial-boundary values problem in the theory of strain gradient thermoelasticity. With the help of an identity of Lagrange’s type, we then prove some theorems regarding the uniqueness of the solution of this mixed problem and also two results regarding the continuous dependence of solutions on initial data and on the charges. We must ouline that we obtain these qualitative results without recourse to any laws of conservation of energy and without recourse to any boundedness assumptions on the coefficients. It is equally important to note that we do not impose restrictions on the elastic coefficients regarding their positive definition.

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