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We consider the mixed problem with boundary and initial data in thermoelasticity of porous bodies with dipolar structure. By generalizing some known results developed by Dafermos in a more simple case of the classical theory of elasticity, we prove new theorems in which we address the issues regarding the uniqueness and existence of a solution with finite energy of the respective problem after we define this type of solution.

The mixed initial-boundary value problem in the context of elasticity of porous bodies having a dipolar structure is considered. By means of a semigroup of contractions, we can obtain some results regarding the existence and uniqueness of solutions for this mixed problem, after proving the equivalence between this problem and a Cauchy problem attached to an abstract equation of evolution. Also, by means of this Cauchy problem, we deduce two continuous dependence results, regarding the supply terms of the original mixed problem and upon initial data.

In this study we formulate the mixed initial boundary value problem for a dipolar thermoelastic material whose micro-particles possess microtemperatures. Then this mixed problem is transformed in a Cauchy problem attached to a temporally equation of evolution on a specific Hilbert space, which will be suitably chosen. As such, we will be able to use certain results specific to the theory of the semigroups of contractions in order to obtain the existence and uniqueness of the solution for our problem. The theory of semigroups also facilitates our approach regarding the continuous dependence of the solution upon initial data and loads. Finally, we reduce our model to the isotropic case and perform numerical simulations for the corresponding system of partial differential equations by means of the finite element method.

A body with a dipolar structure is considered. For the points of such a body are taken into account the microtemperatures and the microrotational effects are neglected. The presence of microtemperatures due to the intimate structure of the environment, who joins to the classical temperature and displacements, does not essentially affect the existence of a generalized solution, nor its uniqueness. In this context, we can generalize a Dafermos type result for a dynamical theory of an inhomogeneous and anisotropic body.

In this study, we will prove that the presence of the voids and of the internal state variables in an elastic body with dipolar structure have no effect on the result of uniqueness regarding the solution of the initial-boundary value problem from this context. First, we put down the basic equations and conditions which define the initial-boundary value problem in the context. Then, by means of three theorems, we prove some auxiliary estimates that underlie the result of uniqueness. Finally, by means of these estimates and by using the Gronwall’s inequality, we prove our main result.

Our study is dedicated to the problem with initial and boundary conditions in the theory of thermoelasticity for micropolar materials with pores. We obtain some results regarding the existence and uniqueness of a finite energy solution of this mixed problem by generalizing the corresponding results obtained by Dafermos in the context of classical elasticity. In some specific conditions we prove some properties regarding the possibility to control the finite energy solution.

In our study, we formulate the boundary value problem in the context of the nonlinear theory of dipolar, porous, and elastic materials. For this problem, some existence and uniqueness results are p...

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.

The main concern of this study is an extension of some results, proposed by Green and Lindsay in the classical theory of elasticity, in order to cover the theory of thermoelasticity for dipolar bodies. For dynamical mixed problem we prove a reciprocal theorem, in the general case of an anisotropic thermoelastic body. Furthermore, in this general context we have proven a result regarding the uniqueness of the solution of the mixed problem in the dynamical case. We must emphasize that these fundamental results are obtained under conditions that are not very restrictive.

In our study, we define the linear backward in time problem for a thermoelastic body with a dipolar structure. In our first main result, we prove the uniqueness of the solution for this problem. Afterward, the issue of locating solutions of the backward in time problem in time will be approached as a consequence of the uniqueness result. In fact, we address the question of the impossibility of locating the solution of this problem in time.

This study deals with the first initial boundary value problem in elasticity of piezoelectric dipolar bodies. We consider the most general case of an anisotropic and inhomogeneous elastic body having a dipolar structure. For two different types of restrictions imposed on the problem data, we prove two results regarding the uniqueness of solution, by using a different but accessible method. Then, the mixed problem is transformed in a temporally evolutionary equation on a Hilbert space, conveniently constructed based on the problem data. With the help of a known result from the theory of semigroups of operators, the existence and uniqueness of the weak solution for this equation are proved.

Composites with microstructure display nonlocal effects and can be effectively modeled through dipolar elasticity. A mixed initial boundary problem is addressed for dipolar thermoelasticity. The basic equations and conditions of the problem are set-up and uniqueness results are proven, which are obtained without introducing definiteness restrictions on the elastic coefficients and, also, without the usual condition imposed to the heat conductivity tensor of being positive definite. An additional result is finally obtained, namely, a reciprocal identity of the Betti's type which underlies another uniqueness result obtained again under weak restrictions.

We consider a time differential model for dual-phase-lag thermoelastic dipolar material. For the heat flux with dual-phase-lag we introduce a time differential equation to describe the thermal effects, and this is coupled with elastic deformation. Some qualitative results on solutions of the mixed initial boundary value problem, associated with this model, are obtained under mild constitutive restrictions. We will deduce an identity of Lagrange type and will use a conservation law in order to prove the uniqueness of solution, whereas the result of continuous dependence of solution is established by using a Gronwall type inequality and a conservation law.

In this paper we investigate the theory of micropolar thermoelastic bodies whose micro-particles possess microtemperatures. We transform the mixed initial boundary value problem into a temporally evolutionary equation on a Hilbert space and after that we prove the existence and uniqueness of the solution. We also approach the study of the continuous dependence of solution upon initial data and loads.

We first formulate the mixed backward in time problem in the context of thermoelasticity for dipolar materials. To prove the consistency of this mixed problem, our first main result is regarding the uniqueness of the solution for this problem. This is obtained based on some auxiliary results, namely, four integral identities. The second main result is regarding the temporal behavior of our thermoelastic body with a dipolar structure. This behavior is studied by means of some relations on a partition of various parts of the energy associated to the solution of the problem.

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.

In this study, we address the mixed initial boundary value problem in the elastostatics of dipolar bodies. Using the equilibrium equations, we build the operator of dipolar elasticity and prove that this operator is positively defined even in the general case of an elastic inhomogeneous and anisotropic dipolar solid. This helps us to prove the existence of a generalized solution for first boundary value problem and also the uniqueness of the solution. Moreover, relying on this property of the operator of dipolar elasticity to be positively defined, we can apply the known variational method proposed by Mikhlin.

This study is dedicated to a micropolar porous body, including voidage time derivative among the independent constitutive variables. We formulate a heat-flux theory in this context taking into account a new set of state variables that includes the heat-flux vector and an evolution equation for it. The mixed initial boundary value problems have the specific feature that the governing system of equations consists of hyperbolic field equations only. Consistency of the theory is supported by a result of uniqueness.

The study of the mixed initial-boundary value problem, corresponding to the thermoelasticity of porous micromorphic materials under the influence of microtemperatures, represents the main objective of this article. Achieving qualitative results on the existence, uniqueness and continuous dependence on the initial data and loads, of the solution of the mixed problem, implies a new perspective of approaching these topics, imposed by the large number of unknowns, which increases the complexity of equations and conditions that characterize the thermoelastic porous micromorphic materials with microtemperatures. The use of the semigroup theory of operators represents the optimal solution for deducing these results, the theory being adaptable to the requirements of the demonstrations, the mixed problem turning into a problem of Cauchy type, with regards to an equation of evolution on a Hilbert space, chosen appropriately.

In this study we approach a mixed initial-boundary value problem to modeling a three-phase-lag dipolar thermoelastic body. The constitutive laws in this context are given. We establish a uniqueness result and prove a reciprocal theorem. The variational principle obtained in this context is a generalization of the known Gurtin’s principle for classical elasticity.

In this paper we derive some identities for the solution of the problem of homogeneous and anisotropic micropolar thermoelasticity. These can be applied to proving uniqueness of the solution of the corresponding boundary initial value problem.

Using the procedure suggested by Dafermos, we are expanding the classical and known Visik's result and prove the existence and uniqueness of a finite energy solution, in the context of the thermoelasticity of porous materials. Also, some additional smoothness assumptions required for the controllability of this solution are investigated.

International audience; This paper is concerned with the theory of thermoelastic dipolar bodies which have a double porosity structure. In contrast with previous papers dedicated to classical elastic bodies, in our context the double porosity structure of the body is influenced by the displacement field, which is consistent with real models. In this setting, we show instability of solution as the initial energy is negative while under an appropriated (and realistic) condition, we prove existence and uniqueness of solution using semi-group theory.

Our study is concerned with the mixed initial-boundary value problem for a dipolar body in the context of a heat-flux dependent theory for the dipolar thermoelastic bodies. We take into account a set of independent constitutive variables including the heat flux vector. Also, the set of basic equations which govern the behavior of such a body is completed by including an equation of evolution for the components of this vector. The uniqueness result, regarding the solution of the mixed problem, which concludes our study assures the consistency of the constructed theory.

In this paper we apply the theory of semigroups of operators in order to obtain the existence and uniqueness of solutions for the mixed initial-boundary value problems in thermoelasticity of dipolar bodies. The continuous dependence of the solutions upon initial data and supply terms is also proved.

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.

This paper applies a new method, thus ensuring the uniqueness of solution for the initial-boundary value problem in thermoelasticity of micropolar bodies with internal state variables. The method of proof is one based upon a Gronwall type inequality.

This article is dedicated to the uniqueness of a solution of the initial boundary value problem in elastodynamics of dipolar bodies with voids. The proofs of theorems are obtained without recourse either to an energy conservation law or to any boundedness assumptions on the elastic coefficients.

This work consists of basic equations and conditions of theory of micropolar bodies with voids. The initial-boundary value problem, in this context, is formulated. Moreover, some basic results of equilibrium are presented.