Title: Mathematical analysis of a constrained parabolic free boundary problem describing droplet motion on a surface

Authors: Karel Svadlenka and Seiro Omata

Issue: Volume 58 (2009), Issue 5, 2073-2102

Abstract: A parabolic free boundary problem with an obstacle and a volume constraint is analyzed. The equation models slow motion of droplets on nonhomogeneous surfaces. We show existence and H\"older continuity of a unique weak solution by a combination of smoothing and a variational method called discrete Morse flow. This method can be directly applied to numerical computation.