Finite-time blow-up of L^{∞} Weak solutions of an aggregation equation

Jeremy Brandman UCLA Department of Mathematics

                       jbrandma@ucla.edu

Abstract: In recent years, the integrodifferential equation u_{t} + ∇ · [(∇K) ∗ 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} ∫ L^{∞}. 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.