Calculus of Variations and Geometric Measure Theory
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P. R. A. S. A. N. T. A. K. U. M. A. R. BARIK

Existence of mass-conserving weak solutions to the singular coagulation equation with multiple fragmentation

created by barik1 on 18 Nov 2018

[BibTeX]

preprint

Inserted: 18 nov 2018

Year: 2018

ArXiv: 1811.06161 PDF

Abstract:

In this paper we study the continuous coagulation and multiple fragmentation equation for the mean-field description of a system of particles taking into account the combined effect of the coagulation and the fragmentation processes in which a system of particles growing by successive mergers to form a bigger one and a larger particle splits into a finite number of smaller pieces. We demonstrate the global existence of mass-conserving weak solutions for a wide class of coagulation rate, selection rate and breakage function. Here, both the breakage function and the coagulation rate may have algebraic singularity on both the coordinate axes. The proof of the existence result is based on a weak L1 compactness method for two different suitable approximations to the original problem, i.e. the conservative and non-conservative approximations. Moreover, the mass-conservation property of solutions is established for both approximations.

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