Oct 12 2009 - 4:30pm - 5:30 pm
CH 240
Barbara Lee Keyfitz (OSU)
"Connections in Conservation Laws: How Hodograph Transforms,
Fourier Transforms and Sturm-Liouville Theory Come Together to
Solve an Elementary Problem in Multidimensional Theory"
A significant difficulty in extending the theory of
hyperbolic conservation laws beyond a single space dimension is
identifying the singularities in solutions that may appear in
multidimensional problems.
Recent numerical results have
suggested that even within the much more restricted set of
self-similar solutions there may be phenomena that are very
complicated indeed -- apparently well beyond the reach of
current analysis.
However, while searching for a simple
prototype, I have come across a problem that is simple and
natural. It appears to have something new to say even about
the classical problem of steady transonic flow, and the solution
uses the familiar tools named in the title.
The problem and its solution will be expounded in two
talks, to an audience that is not assumed to have any prior
acquaintance with the theory of conservation laws.
This lecture is part of
Invitation to Mathematics.
Pre-candidacy students can sign up for this lecture series by registering for one credit hour of
Math 693, Call # 27103 (with Prof H. Moscovici).