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Abstract
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.
Mes nagrinejame matematini modeli, kuris aprašo salyti tarp pjezoelektriko ir kli uties. Laikoma, kad medžiaga yra elektroelastine ir nusakoma netiesiniu elastingumo operatoriumi. Salytis modeliuojamas remiamtis sausos trinties Coulomb'o desniu, kuriame trinties koeficientas priklauso nuo slydimo. Mes gavome variacini modelio formulavima lygčiu sistemos formoje, kurios nežinomaisiais yra perkeltasis laukas ir elektrinis potencialas. Irodomas sprendinio silpnaja prasme egzistavimas ir su nedidelemis prielaidomis vienatis. Irodymas paremtas rezultatais gautais [14] darbe, kuriame tiriamos elipsines kvazivariacines nelygybes.