Taranets R. Qualitative analysis of higher-order nonlinear parabolic equations and systems

This thesis is devoted to the study of solvability and qualitative behaviour of generalised solutions to initial boundary value problems for high-order nonlinear pa¬ra¬bo¬lic equations and systems which arise in the modelling of various processes in hydrodynamics, material science, medicine and biology. The scientific importance of thin liquid film modelling originates from numerous industrial applications. These include: detergency and aerosol delivery of medicating drugs, coating flow technology, film drainage in emulsions and foams, drying of semi-conductor wafers in microelectronics, manufacturing of printed electronics and ink jet printing. The modern areas of microfluidics and nanofluidics naturally call upon techniques associated with thin fluid films, such as the operation of microfluidic devices and the ordered growth of nano-tubes and nanowires. When a thin liquid film (of thickness less than 100 nm) dewets on a solid surface, intermolecular forces (e.g., van der Waals and gravitational forces) play a central role in driving the flow. If the solid surface is chemically patterned, gradients in wettability serve as an additional driving force for the flow. This additional feature leads to more complex behaviour and dynamics, and makes the study of thin liquid films on chemically patterned surfaces a particularly rich experimental topic.