ABSTRACT
A central issue in the use of C-F models is their potential to provide predicted outcomes through the qualitative information that can be retrieved from their analysis. A similar issue can be raised for the fragmentation equation and the quest for self-similar solutions also requires some homogeneity assumptions on the fragmentation coefficients. The mass-conserving self-similar profile behaves for small sizes exactly as predicted. The derived large size behaviour is less precise than the expected decay but reveals that it cannot be faster than exponential. The chapter discusses the detailed balance condition is far from being universal and that most choices of coagulation and fragmentation coefficients do not have such a property. The behaviour of solutions to the C-F equation is then widely open in general, though stationary solutions can be constructed for some classes of coefficients.
