A variational approach to a quasi-static droplet model

Grunewald, Natalie; Kim, Inwon
May 2011
Calculus of Variations & Partial Differential Equations;May2011, Vol. 41 Issue 1/2, p1
Academic Journal
We consider a quasi-static droplet motion based on contact angle dynamics on a planar surface. We derive a natural time-discretization and prove the existence of a weak global-in-time solution in the continuum limit. The time discrete interface motion is described in comparison with barrier functions, which are classical sub- and super-solutions in a local neighborhood. This barrier property is different from standard viscosity solutions since there is no comparison principle for our problem. In the continuum limit the barrier properties still hold in a modified sense.


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