An ill-posed mechanical problem with friction
Résumé
Many models involve the Coulomb's law in order to describe dynamical properties of friction phenomena. In order to generalize this Coulomb's law and to deal with its correct mathematical expression, we study a nonlinear equation where we take into account a maximal monotone graph. In the particular case of Coulomb's law, existence and uniqueness are proved. But in the general case, only existence persists. A counter-example to uniqueness is given.