Workshop
Existence and asymptotic behaviour of solutions for a non-local thin-film equation
- Roman Taranets (Institute of Applied Mathematics and Mechanics of the NAS of Ukraine)
Abstract
We prove existence of solutions to a family of fractional thin-film equations in a bounded domain. A non-local operator is given by the spectral fractional Laplacian. In the case of a "strong slippage" regime with "complete wetting" interfacial conditions, we prove local entropy estimates which entails finite speed of propagation of the support and a lower bound for the waiting time phenomenon.
