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Investigation of mathematical models for thin-film flows (TFE)
Start date: Oct 8, 2012, End date: Oct 7, 2013 PROJECT  FINISHED 

"This research project will bring together Dr Roman Taranets, an outstanding young researcher at the Ukrainian National Academy of Sciences, and Professor John King, a leading expert in the theory of thin film flows at Nottingham University, UK. The research will be focussed on flows of thin liquid and polymer films. The combination of Dr Taranets’ background in research methods for the rigorous investigation of the qualitative properties of solutions to nonlinear partial differential equations and the host’s expertise in formal asymptotic methods and contacts with a range of industry-driven applications will be an ideal basis for a successful fellowship.During the research project, we will• study exact asymptotic behaviour travelling wave solutions for the thin film equation with non-zero contact angles;• show the existence of a generalized solution for multi-dimensional coating flow models without surfactant and to investigate the behaviour of support of these solutions;• investigate the asymptotic behaviour of generalized solutions for multi-dimensional coating flows with surfactant;• put in place additional research programmes involving novel areas of application and employing innovative combinations of mathematical techniques.Benefits of this transfer of knowledge will include the implementation of the collaborative research programmes above, the initial training of both early-career researchers in the UK and Dr Taranets in complementary mathematical approaches and the application of these unusual combinations of skills to a host of applications that are representative of the many fields in which high-order parabolic systems are now playing a central role. Moreover, ongoing collaborations between the Ukrainian and UK groups will provide a conduit for the continued expansion of the scope of these research activities. The ERA will benefit from proposed fellowship due to access to new approaches and methods for studying nonlinear PDEs."
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