Asymptotics behaviour in one dimensional model of interacting particles

We consider the equation u_t=\epsilon u_{xx}+(u\ K'*u)_x for x\in\mathbb{R}, t>0 and with \epsilon\geq 0, supplemented with a nonnegative, integrable initial datum. We present a class of interaction kernels K' such that the large time behaviour of solutions to this initial value problem is described by a compactly supported self-similar profile.