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On the breakage problem with a homogeneous erosion type kernel. (English) Zbl 0978.82516

Summary: The breakage equation with a homogeneous erosion type kernel is studied herein. This type of kernel renders the handling of the breakage equation by conventional techniques very difficult, necessitating alternative problem solving approaches. Exploiting the structure of the erosion-breakage kernel, a new particle erosion equation is derived as the first-order term of a formal 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 order to overcome this difficulty, the problem is decomposed into a system of equations for the size distribution of the generations of fragments which admits unimodal solutions. The properties and the methods of solution (analytical, method of moments, etc) are studied extensively. Using solution techniques developed in this paper, results are reported for some simple cases, revealing a very interesting and rather unusual structure of the solutions of the erosion-breakage equation.

MSC:

82C99 Time-dependent statistical mechanics (dynamic and nonequilibrium)
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