The Experts below are selected from a list of 210 Experts worldwide ranked by ideXlab platform
Cătălin Galeş - One of the best experts on this subject based on the ideXlab platform.
-
On uniqueness and continuous dependence of solutions in viscoelastic mixtures
Meccanica, 2010Co-Authors: Cătălin Galeş, Ionel-dumitrel GhibaAbstract:This note deals with the isothermal linear theory of porous viscoelastic mixtures. Questions of uniqueness and continuous dependence for solutions of various classes of initial boundary value problems in mixtures consisting of two constituents: a porous elastic solid and a porous Kelvin–Voigt material are studied. The Lagrange Identity and Logarithmic convexity methods are used to establish uniqueness and continuous dependence results, with no definiteness assumptions upon the internal energy.
-
Some uniqueness and continuous dependence results in the theory of swelling porous elastic soils
International Journal of Engineering Science, 2002Co-Authors: Cătălin GaleşAbstract:This paper is concerned with the isothermal linear theory of swelling porous elastic soils. Initial-boundary value problems are formulated for the linear dynamic theory of an isothermal mixture consisting of three components: an elastic solid, a viscous fluid and a gas. Then the uniqueness and continuous dependence problems are discussed in connection with the solutions of such initial-boundary value problems. The uniqueness results are established under mild positive semi-definiteness assumptions or with no definiteness assumptions upon the internal energy. Various estimates are established for describing the continuous dependence of solutions with respect to the external given data. In this aim the Lagrange Identity and the logarithmic convexity methods are used.
Marin Marin - One of the best experts on this subject based on the ideXlab platform.
-
An approach with Lagrange Identity of the mixed problem in theory of strain gradient thermoelasticity
ITM Web of Conferences, 2020Co-Authors: Marin MarinAbstract: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.
-
The mixed problem in the theory of strain gradient thermoelasticity approached with the Lagrange Identity
Boundary Value Problems, 2020Co-Authors: Marin Marin, Sorin Vlase, Ioan TunsAbstract:In our paper we address the thermoelasticity theory of the strain gradient. First, we define the mixed problem with initial and boundary data in this context. Then, with the help of an Identity of Lagrange type, we prove some uniqueness theorems with regards to the solution of this problem and two theorems with regards to the continuous dependence of solutions on loads and on initial data. We want to highlight that the use of the approach proposed in this work enables obtaining results without recourse to any boundedness assumptions on the coefficients or to any laws of conservation of energy. Also, we do not impose restrictions on thermoelastic coefficients regarding their positive definition.
-
Implications of the Lagrange Identity in Thermoelasticity of Dipolar Bodies
Advanced Structured Materials, 2019Co-Authors: Marin Marin, Andreas Öchsner, Sorin VlaseAbstract:This paper is concerned with the mixed initial-boundary value problem in the context of the theory of thermoelasticity of dipolar bodies. We prove a uniqueness theorem and some continuous dependence theorems without recourse to any energy conservation law, or to any boundedness assumptions on the thermoelastic coefficients. This was possible due to the use of Lagrange’s Identity. Because of the flexibility of this Identity, we also avoid the use of positive definiteness assumptions on the thermoelastic coefficients.
-
nonsimple material problems addressed by the Lagrange s Identity
Boundary Value Problems, 2013Co-Authors: Marin Marin, Ravi P Agarwal, Sr MahmoudAbstract:Our paper is concerned with some basic theorems for nonsimple thermoelastic materials. By using the Lagrange Identity, we prove the uniqueness theorem and some continuous dependence theorems without recourse to any energy conservation law, or to any boundedness assumptions on the thermoelastic coefficients. Moreover, we avoid the use of positive definiteness assumptions on the thermoelastic coefficients.
-
Lagrange Identity method for microstretch thermoelastic materials
Journal of Mathematical Analysis and Applications, 2010Co-Authors: Marin MarinAbstract:Our paper is concerned with some basic theorems for microstretch thermoelastic materials. By using the Lagrange Identity, we prove the uniqueness theorem and some continuous dependence theorems without recourse to any energy conservation law, or to any boundedness assumptions on the thermoelastic coefficients. Moreover, we avoid the use of positive definiteness assumptions on the thermoelastic coefficients.
Salvatore Rionero - One of the best experts on this subject based on the ideXlab platform.
-
Lagrange Identity IN LINEAR VISCOELASTICITY
2016Co-Authors: S. Chiritii, Salvatore RioneroAbstract:(Communicated by E. SOOS) Abstract-An approach based on the Lagrange Identity is developed for the study of the initial boundary value problems of linear vi~oelasticity. estimations are obtained for describing the Liapunov stability and continuous data dependence of solutions. The main differences between the respective stimates consist in the measure of continuity and the constraint sets on which they are valid. The Lagrange identities are also used in order to obtain some reciprocal relations. The Cesaro means and autocorrelations of the velocity field and the strain field are introduced and it is proved that they exist and have a common value. 1
-
Lagrange Identity in linear viscoelasticity
International Journal of Engineering Science, 1991Co-Authors: Stan Chiriţă, Salvatore RioneroAbstract:Abstract An approach based on the Lagrange Identity is developed for the study of the initial boundary value problems of linear viscoelasticity. Estimations are obtained for describing the Liapunov stability and continuous data dependence of solutions. The main differences between the respective estimates consist in the measure of continuity and the constraint sets on which they are valid. The Lagrange identities are also used in order to obtain some reciprocal relations. The Cesaro means and autocorrelations of the velocity field and the strain field are introduced and it is proved that they exist and have a common value.
Ionel-dumitrel Ghiba - One of the best experts on this subject based on the ideXlab platform.
-
On uniqueness and continuous dependence of solutions in viscoelastic mixtures
Meccanica, 2010Co-Authors: Cătălin Galeş, Ionel-dumitrel GhibaAbstract:This note deals with the isothermal linear theory of porous viscoelastic mixtures. Questions of uniqueness and continuous dependence for solutions of various classes of initial boundary value problems in mixtures consisting of two constituents: a porous elastic solid and a porous Kelvin–Voigt material are studied. The Lagrange Identity and Logarithmic convexity methods are used to establish uniqueness and continuous dependence results, with no definiteness assumptions upon the internal energy.
Petr Zemanek - One of the best experts on this subject based on the ideXlab platform.
-
Time scale symplectic systems with analytic dependence on spectral parameter
Journal of Difference Equations and Applications, 2015Co-Authors: Roman Simon Hilscher, Petr ZemanekAbstract:This paper is devoted to the study of time scale symplectic systems with polynomial and analytic dependence on the complex spectral parameter λ. We derive fundamental properties of these systems (including the Lagrange Identity) and discuss their connection with systems known in the literature, in particular with linear Hamiltonian systems. In analogy with the linear dependence on λ, we present a construction of the Weyl disks and determine the number of linearly independent square integrable solutions. These results extend the discrete time theory considered recently by the authors. To our knowledge, in the continuous time case this concept is new. We also establish the invariance of the limit circle case for a special quadratic dependence on λ and its extension to two (generally nonsymplectic) time scale systems, which yields new results also in the discrete case. The theory is illustrated by several examples.
-
Generalized Lagrange Identity for Discrete Symplectic Systems and Applications in Weyl–Titchmarsh Theory
Springer Proceedings in Mathematics & Statistics, 2014Co-Authors: Roman Simon Hilscher, Petr ZemanekAbstract:In this paper we consider discrete symplectic systems with analytic dependence on the spectral parameter. We derive the Lagrange Identity, which plays a fundamental role in the spectral theory of discrete symplectic and Hamiltonian systems. We compare it to several special cases well known in the literature. We also examine the applications of this Identity in the theory of Weyl disks and square summable solutions for such systems. As an example we show that a symplectic system with the exponential coefficient matrix is in the limit point case.
-
generalized Lagrange Identity for discrete symplectic systems and applications in weyl titchmarsh theory
2014Co-Authors: Roman Simon Hilscher, Petr ZemanekAbstract:In this paper we consider discrete symplectic systems with analytic dependence on the spectral parameter. We derive the Lagrange Identity, which plays a fundamental role in the spectral theory of discrete symplectic and Hamiltonian systems. We compare it to several special cases well known in the literature. We also examine the applications of this Identity in the theory of Weyl disks and square summable solutions for such systems. As an example we show that a symplectic system with the exponential coefficient matrix is in the limit point case.
