

Martin Brokate: On uniqueness in evolution quasivariational inequalities
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 classical
isotropic and kinematic hardening, as for example in
the Gurson model.
