ABSTRACT
This chapter discusses the solvability of the fragmentation equations considered as abstract Cauchy problems posed in an appropriate state space so that the semigroup techniques can be employed. One of the main difficulties in the analysis of fragmentation processes is that they simultaneously involve the evolution of two intertwined quantities: the masses of the particles and their numbers. The chapter considers processes in which mass should be conserved due to the fact that the fragmentation process only rearranges the distribution of mass among particles. However, in many situations, fragmentation occurs alongside processes that involve loss or gain of mass. Mass loss can result from oxidation, melting, sublimation, and dissolution of the matter on the exposed surface of the particles. Also, the resulting surface recession widens the pores of the particles causing loss of connectivity and fragmentation as the bridges between the pores break and the pores join each other.
