Optimal control of differential quasivariational inequalities with applications in contact mechanics

SOFONEA, MIRCEA; BOLLATI, JULIETA; TARZIA, DOMINGO A.

JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS

ACADEMIC PRESS INC ELSEVIER SCIENCE

Año: 2021 vol. 493 p. 1 - 23

0022-247X

We consider a differential quasivariational inequality for which we state and prove the continuous dependence of the solution with respect to the data. This convergence result allows us to prove the existence of at least one optimal pair for an associated control problem. Finally, we illustrate our abstract results in the study of a free boundary problem which describes the equilibrium of a viscoelastic body in frictionless contact with a foundation made of a rigid body covered by a rigid-elastic layer.