Quasistatic Evolution of Sessile Drops and Contact Angle Hysteresis

We consider the classical model of capillarity coupled with a rate-independent dissipation mechanism due to frictional forces acting on the contact line, and prove the existence of solutions with prescribed initial configuration for the corresponding quasistatic evolution. We also discuss in detail some explicit solutions to show that the model does account for contact angle hysteresis, and to compare its predictions with experimental observations.