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{\it Finite-time blow-up of $L^{\infty}$ Weak solutions of an
aggregation equation} 

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{\bf Jeremy Brandman}\\
UCLA\\
Department of Mathematics\\
{\tt jbrandma@ucla.edu}
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\noindent {\bf Abstract}:  In recent years, the integrodifferential equation
$u_t + \nabla \cdot  [(\nabla K)\ast u)u] = 0$ 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
$L^1 \int L^{\infty}$.  For kernels $K$ which are rotationally
invariant, nonnegative, and decay at infinity, finite-time blow-up is
proven when $K$ has a Lipschitz point at the origin. 

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