B05 – Dynamics of coagulation-fragmention equations
Smoluchowski’s coagulation equation is a basic mean-field model that describes mass aggregation in various applications. During the first two funding periods we mainly addressed the fundamental question of dynamic scaling, that is whether solutions converge for large times to a uniquely determined self-similar solution. One of the main results of this research was, that, quite surprisingly, the long-time behavior is in general not universal, but depends on details of the coagulation kernel. In particular, if the kernel is diagonally dominant, one obtains concentration into oscillating peak solutions. We will continue these investigations and also plan to prove for more general models with fragmentation that oscillatory solutions exist. This includes a study of the Becker-Döring model with injection of monomers and removal of large clusters. In a certain asymptotic limit this problem will allow to consider also space-dependent cases and to study the effect of diffusion or advection on the nucleation mechanism. Furthermore, we will address questions that were raised by applied scientists from aerosol physics. For example, we plan to study the long-time asymptotics of coagulation models with monomer injection, in particular in cases in which steady state solutions do not exist. We will also investigate the properties of stationary and time dependent solutions to multicomponent coagulation and coagulation fragmentation models. In particular we will determine under which conditions the solutions of multicomponent coagulation equation are localized along particular directions in the space of particle compositions. Another goal is to derive asymptotic properties of coagulation kernels which describe coagulation of particles moving in a medium formed by much smaller particles and for which the mean free path is comparable to their particle size.
|Velázquez, Juan José||IAM||En60email@example.com|