Free Boundary Problems 2026

Asymptotic behavior of solutions to the nonlinear degenerate PDEs describing evolution of thin viscous sheets

9 Sept 2026, 12:00

30m

Main building/Floor 1-Room 2094 - Lecture Hall (HU (Main Building))

Hydrodynamic Models with Moving Contact Lines Hydrodynamic Models with Moving Contact Lines

Speaker

Georgy Kitavtsev (Middle East Technical University, Nothern Cyprus Campus)

Description

In this talk, we consider the nonlinear system of coupled degenerate PDEs describing evolution of the free surface of a viscous thin liquid sheet. We show that in the associated Lagrangian coordinates the system transforms to the singular diffusion porous medium type equation equipped with the non-homogeneous in space and time source term having zero mean.
In the regime of vanishing sheet surface tension, we show H^1-exponential asymptotic decay to the flat profile of the solutions to the latter equation considered with general initial data in spatial dimensions d<=3. The results were obtained in joint work with Marco Fontelos and Roman Taranets.