Abstract |

**Thin Films of Non-Newtonian Fluids with
Jump Discontinuities**

*V.Chugunov, L.D.Eskin (Kazan State
University, Kazan, Russia); K.Hutter (Institut fur Mechanik, Technische
Universitat, Darmstadt, Germany)*

*e-mail:
chug@ksu.ru*

Many
physical processes associated with film flows are described by sharp changes of
their main characteristics -- fluid thickness and mass flux in some small
regions. In such situations it is natural to consider models which allow
solutions in which a field variable or its space or time derivative may
experience a jump discontinuity. Solutions with jumps are natural for
hyperbolic equations, and their existence is evident. The situation is
different when more complex models, described by parabolic equations, are
considered. In this case, the existence of a solution with jumps is not
evident. Let us restrict attention to
models describing the "diffusive" spreading of a film, which starts
initially with a jump in its surface elevation. This choice is motivated by the
following reasoning. First, one particular model demonstrates that, if the
boundary conditions are regular, then the solution is smooth, even for an
initially discontinuous surface elevation; second, such models describe
possible realistic situations, and third, they possess certain symmetries
allowing a qualitative analysis.
Therefore, we can formulate the aim of this work: to consider models
admitting the symmetry, in order to show existence of solutions with jumps and
to discuss their physical interpretation.

Section
: 12