Department of Mathematics
Center for Research in Scientific Computation
North Carolina State University
I will review progress in understanding experimental and numerical observations of wave patterns in the flow of thin films driven by a temperature gradient. This project culminated in the use of both a kinetic relation for undercompressive shocks, and a nucleation condition to distinguish between long-time attractors for the PDE. In more recent work, a surfactant concentration gradient provides the driving force. Here, certain traveling waves are overcompressive. These waves present a challenge for stability analysis, but there are some hints from experiments of Troian, and numerical studies of Craster and Matar.