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Asymptotic decay towards steady states of solutions to very fast and singular diffusion equations
Georgy Kitavtsev, Roman M. Taranets
We analyze long-time behavior of solutions to a class of problems related to very fast and singular diffusion porous medium equations having nonhomogeneous in space and time source…
Long-time behaviour of solutions to a singular heat equation with an application to hydrodynamics
Georgy Kitavtsev, Roman M. Taranets
In this paper, we extend the results of [1] by proving exponential asymptotic -convergence of solutions to a one-dimensional singular heat equation with -source term that…
Weak solutions to lubrication systems describing the evolution of bilayer thin films
Sebastian Jachalski, Georgy Kitavtsev, Roman Taranets
The existence of global nonnegative weak solutions is proved for coupled one-dimensional lubrication systems that describe the evolution of nanoscopic bilayer thin polymer films th…
Stationary solutions of liquid two-layer thin film models
Sebastian Jachalski, Robert Huth, Georgy Kitavtsev +2
We investigate stationary solutions of a thin-film model for liquid two-layer flows in an energetic formulation that is motivated by its gradient flow structure. The goal is to ach…
Weak solutions to lubrication equations in the presence of strong slippage
Georgy Kitavtsev, Philippe Laurencot, Barbara Niethammer
The existence of global weak solutions is proved for one-dimensional lubrication models that describe the dewetting process of nanoscopic thin polymer films on hydrophobyzed substr…