  This work is devoted to the study of a relaxation limit of the so-called
aggregation equation with a pointy potential in one dimensional space. The
aggregation equation is by now widely used to model the dynamics of a density
of individuals attracting each other through a potential. When this potential
is pointy, solutions are known to blow up in final time. For this reason,
measure-valued solutions have been defined. In this paper, we investigate an
approximation of such measure-valued solutions thanks to a relaxation limit in
the spirit of Jin and Xin. We study the convergence of this approximation and
give a rigorous estimate of the speed of convergence in one dimension with the
Newtonian potential. We also investigate the numerical discretization of this
relaxation limit by uniformly accurate schemes.
