Abstract: The theory of O.D.E's is mainly concerned with equations of the
form
x'= f(t,x)
with smooth right hand side. However, there are some
important cases where discontinuous O.D.E's arise, namely:
1. the equations of characteristics, for discontinuous solutions to
conservation laws,
2. feedback controls.
The talk will survey various concepts of
solutions to discontinuous O.D.E's,
present the main results concerning the existence and the
topological properties of the solution set,
and discuss some applications.
The talk will remain for the most part at a very elementary level.
As a prerequisite, only basic O.D.E. theory is required.
Helge Holden <holden@math.ntnu.no>
2000-11-03 18:04