This talk is concerned with the stability and asymptotic stability at large time of solutions to a system of equations, which includes the Lifschitz-Slyozov-Wagner (LSW) system in the case when the initial data has compact support. The main result is a proof of weak global asymptotic stability for LSW like systems. Comparison to a quadratic model plays an important part in the proof of the main theorem when the initial data is critical. The quadratic model extends the linear model of Carr and Penrose. This is joint work with Barbara Niethammer.