Existence and uniqness of solution to the Lifshitz-Slyozov system with monomers spatial diffusion
Seminar Room 1, Newton Institute
The standard Lifshitz-Slyozov model describes the evolution of a population of macro-particles or polymers immersed in a bath of monomers. It appears in such solution interaction phenomena between macro-particles characterized by their size density repartition f (t, ξ ) and the monomers characterized by their concentration c(t). These interactions induce the growth of large particles at the expense of the smaller ones what is known as Ostwald ripening. The evolution dynamic is governed by partial diﬀerential equations.
We extend this standard model to a more complexe one taking into account the spatial diﬀusion of the monomers concentration. So we prove the existence and uniqueness of solution for the model.