# On uniqueness in evolution quasivariational inequalities

## Prof. Dr. Martin Brokate

Jan. 23, 2003, 3:30 p.m. T 911

We consider a rate independent evolution quasivariational inequality in a Hilbert space X with closed convex constraints having nonempty interior. We prove that there exists a unique solution which is Lipschitz dependent on the data, if the gradient of the square of the Minkowski functional of the convex constraint is Lipschitz continuous, and if the overall Lipschitz constant is small enough. We exhibit an example of nonuniqueness if this condition is violated. The result aims at applications to elastoplastic constitutive laws where the yield surface depends on the loading history in a more complex manner than in the classical isotropic and kinematic hardening.