Strong solutions to diffusive coagulation-fragmentation equations

Christoph Walker Vanderbilt University, Nashville, USA

We consider a coupled system of uncountably many equations of reaction-diffusion type, which describes the time evolution of particles of different sizes undergoing coagulation and fragmentation. Our approach allows us to treat simultaneously the classical model, where particles may grow unrestricted, and a variant thereof including a maximal particle size. Besides uniqueness and local in time existence of smooth solutions, we derive global existence in particular cases, e.g. for small initial values in the absence of fragmentation.