#
Nonlinear PDEs of mixed type arising in mechanics and geometry

March 17 to March 21, 2008
at the

American Institute of Mathematics,
Palo Alto, California

organized by

Gui-Qiang Chen,
Tai-Ping Liu,
Richard Schoen,
and Marshall Slemrod

## Original Announcement

This workshop will be devoted to
the study of nonlinear partial differential equations of mixed
hyperbolic and elliptic type arising in conservation laws,
continuum mechanics, differential geometry, relativity,
and string theory.
In the past two years there has been a surge of activity on nonlinear
partial differential equations of mixed type where the problems that
had long lain dormant because of lack of new ideas have been
successfully attacked. However, the problems that can be studied and
should be studied are much more general that what has been done so
far. For example, the simple act of crumpling a piece of paper can
be modeled as a "transonic" problem which possesses all the
intuition gained by everyday experience and all the difficulty of
systems of conservation laws exhibiting change of type. The
"transonic" nature comes from the basic theory of differential
geometry where the original Gauss curvature of the flat paper is
zero and hence must be preserved under the isometry of the crumpling
by Gauss's "theorem egregium". The zero Gauss curvature translates
into making the Gauss-Codazzi system being everywhere sonic. The
sonic problem with a little work can then be made a special case of
more general transonic problems. Of course, many more problems arise
in geometry and mechanics. Some recent publications on isometric
embedding of Riemannian manifolds in Euclidean spaces have more
examples, but ironically paper crumpling or any problems arising
from day to day mechanics is not on their list. This workshop
provides a venue to trade problems, methods, and ideas and to form
new contacts with mathematicians, engineers, physicists, who might
not normally meet in their usual day to day schedule.

## Material from the workshop

A list of participants.
The workshop schedule.

A report on the workshop activities.

Papers arising from the workshop: