Modeling in particular with partial differential equations plays an ever growing role in the
applied sciences. Hence its mathematical understanding is an important issue for today's
research. This book provides an introduction to three different topics in partial differential
equations arising from applications. The subject of the first course by Michel Chipot (Zurich)
is equilibrium positions of several disks rolling on a wire. In particular existence and
uniqueness of and the exact position for an equilibrium are discussed. The second course by
Josselin Garnier (Toulouse) deals with problems arising from acoustics and geophysics where
waves propagate in complicated media the properties of which can only be described
statistically. It turns out that if the different scales presented in the problem can be
separated there exists a deterministic result. The third course by Otared Kavian (Versailles
St.-Quentin) is devoted to so-called inverse problems where one or several parameters of a
partial differential equation need to be determined by using for instance measurements on the
boundary of the domain. The question that arises naturally is what information is necessary to
determine the unknown parameters. This question is answered in different settings. The text is
addressed to students and researchers with a basic background in partial differential
equations.
