MATHEMATICS DEPARTMENT
North Carolina State University

Differential Equations Seminar

Thursday,  October 4,  2001
2:35 p.m.  330 Harrelson Hall

Andrea Bertozzi

Departments of Mathematics and Physics

Duke University

"Dewetting Films: Bifurcations and Concentrations"

Abstract


Under the influence of long range attractive and short range repulsive forces, thin liquid films rupture and form complex dewetting patterns. This paper studies this phenomenon in one space dimension in the framework of fourth order degenerate parabolic equations of lubrication type. We derive the global structure of the bifurcation diagram for steady state solutions. A stability analysis of the solution branches and numerical simulations suggest coarsening occurs. Furthermore, we study the behavior of solutions in the limit that short range repulsive forces are neglected. Both asymptotic analysis and numerical experiments show that this limit can concentrate mass in delta-distributions. This is joint work with Guenther Gruen (Bonn) and Tom Witelski (Duke).


Graduate students are invited to attend