Analysis of a Signorini problem with nonlocal friction in thermo-piezoelectricity

We consider a mathematical model which describes the frictional unilateral contact between a thermo-piezoelectric body and a rigid electrically conductive foundation. The thermo-piezoelectric constitutive law is assumed to be nonlinear and the contact is modeled with the Signorini condition, the nonlocal Coulomb friction law with slip dependent friction coefficient and the regularized electrical and thermal conductivity conditions. The variational form of this problem is a coupled system which consists of a nonlinear variational inequality for the displacement field and two nonlinear variational equations for the electric potential and the temperature. The existence of a unique weak solution to the problem is proved by using abstract results for elliptic variational inequalities and fixed point arguments

Frictional contact problem in dynamic electroelasticity

The dynamic evolution with frictional contact of a electroelastic body is considered. In modelling the contact, the Tresca model is used. We derive a variational formulation for the model in a form of a coupled system involving the displacement and the electric potential fields. We provide existence and uniqueness result. The proof is based on a regularization method, Galerkin method, compactness and lower semicontinuity arguments. Such a result extend the result obtained by Duvaut and Lions, where the analysis of friction in dynamic elasticity materials was provided. The novelty of this paper consists in the fact that here we take into account the piezoelectric properties of the materials

A piezoelectric contact problem with slip dependent coefficient of friction

We consider a mathematical model which describes the static frictional contact between a piezoelectric body and an obstacle. The constitutive relation of the material is assumed to be electroelastic and involves a nonlinear elasticity operator. The contact is modelled with a version of Coulomb's law of dry friction in which the coefficient of friction depends on the slip. We derive a variational formulation for the model which is in form of a coupled system involving as unknowns the displacement field and the electric potential. Then we provide the existence of a weak solution to the model and, under a smallness assumption, we provide its uniqueness. The proof is based on a result obtained in [14] in the study of elliptic quasi‐variational inequalities. Pjezoelektriko sąlyčio su priklausomu nuo slydimo trinties koeficiento uždavinys Santrauka Mes nagrinėjame matematinį modelį, kuris aprašo sąlytį˛ tarp pjezoelektriko ir kliūties. Laikoma, kad medžiaga yra elektroelastinė ir nusakoma netiesiniu elastingumo operatoriumi. Sąlytis modeliuojamas remiamtis sausos trinties Coulomb’o dėsniu, kuriame trinties koeficientas priklauso nuo slydimo. Mes gavome variacinį modelio formulavimą lygčių sistemos formoje, kurios nežinomaisiais yra perkeltasis laukas ir elektrinis potencialas. Įrodomas sprendinio silpnąja prasme egzistavimas ir su nedidelėmis prielaidomis vienatis. Įrodymas paremtas rezultatais gautais [14] darbe, kuriame tiriamos elipsinės kvazivariacinės nelygybės. First Published Online: 14 Oct 201

A viscoelastic contact problem with normal damped response and friction

We study an evolution problem which describes the quasistatic contact of a viscoelastic body with a foundation. We model the contact with normal damped response and a local friction law. We derive a variational formulation of the model and we establish the existence of a unique weak solution to the problem. The proof is based on monotone operators and fixed point arguments. We also establish the continuous dependence of the solution on the contact boundary conditions

Identifying Initial Condition in Degenerate Parabolic Equation with Singular Potential

A hybrid algorithm and regularization method are proposed, for the first time, to solve the one-dimensional degenerate inverse heat conduction problem to estimate the initial temperature distribution from point measurements. The evolution of the heat is given by a degenerate parabolic equation with singular potential. This problem can be formulated in a least-squares framework, an iterative procedure which minimizes the difference between the given measurements and the value at sensor locations of a reconstructed field. The mathematical model leads to a nonconvex minimization problem. To solve it, we prove the existence of at least one solution of problem and we propose two approaches: the first is based on a Tikhonov regularization, while the second approach is based on a hybrid genetic algorithm (married genetic with descent method type gradient). Some numerical experiments are given

Inventaire des prédateurs des acariens Tetranychidae en vergers d'agrumes du Souss au Maroc

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Phytoseiidae et insectes prédateurs associées aux plantes de la réserve de biosphère de l’arganeraie

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