Abstract: In recent years, the integrodifferential equation
has been used to model
biological aggregation and dispersion. During this talk, we discuss
recent work on existence, uniqueness, and finite-time blow-up of
solutions to this equation for nonnegative initial data belonging to
. For kernels
which are rotationally
invariant, nonnegative, and decay at infinity, finite-time blow-up is
proven when
has a Lipschitz point at the origin.