Dynamics and stability of sessile drops with contact points

In an effort to study the stability of contact lines in fluids, we consider dynamics a drop incompressible viscous Stokes fluid evolving above one-dimensional flat surface under influence gravity. This is free boundary problem: interface between on and air (modeled by trivial fluid) move experiences capillary forces. The three-phase where fluid, air, solid vessel wall meet known as point, angle formed called angle. We model this problem that allows for fully dynamic points angles. develop scheme priori estimates model, which then us show initial data sufficiently close equilibrium, admits global solutions decay shifted equilibrium exponentially fast.