On the breakage problem with a homogeneous erosion type kernel

The breakage equation with a homogeneous erosion type kernel is studied her ein. This type of kernel renders the handling of the breakage equation by c onventional techniques very difficult, necessitating alternative problem so lving approaches. Exploiting the structure of the erosion-breakage kernel, a new particle erosion equation is derived as the first-order term of a for mal perturbation expansion with respect to kernel parameters. However, even this new equation is very difficult to treat because of the multimodality of its solution associated with the developing generations of fragments. In older to overcome this difficulty, the problem is decomposed into a system of equations for the size distribution of the generations of fragments whi ch admits unimodal solutions. The properties and the methods of solution (a nalytical, method of moments, etc) are studied extensively. Using solution techniques developed in this paper, results are reported for some simple ca ses, revealing a very interesting and rather unusual structure of the solut ions of the erosion-breakage equation.