A perturbation method for solving a quadratic evolution equation

Abstract

A quadratic evolution equation of the form \[ u ˙ = L u + ϵ Q u \dot u = Lu + \epsilon Qu \] is considered where L L and Q Q are particular linear and quadratic integral operators respectively. This equation has been proposed to describe the variation with time of u ( x , t ) u(x,t) , the volume density of an ensemble of particles undergoing concurrent coalescence and fracture.