## Applied Mathematics Colloquium: Dr. Thomas Seidman

#### UMBC

**Title:** Differential equations with discontinuous right hand side

**Speaker: **Thomas
Seidman, UMBC

**Abstract: **We consider the existence
of solutions of equations of the form y’ = f(y). When f is
Lipschitzian one obtains existence (and uniqueness by Picard iteration (CMP).
When f is only continuous one still (at least in the finite dimensional case)
obtains existence, but not uniqueness (Peano Theorem). Filippov, in the
context of f piecewise smooth with smooth separating surfaces, obtained
existence of a type of generalized solution. [This notion included the
introduction of “sliding modes”, now an essential ingredient of hybrid
control theory.]

The present treatment uses a
somewhat related notion of generalized solution to obtain existence without
imposing any regularity assumption at all on f. [This discussion is an
outcome of collaboration with Mike Jeffrey (Univ.Bristol, UK).]