An existence‐uniqueness result for the pure binary collisional breakage equation

The study of collision‐induced breakage phenomenon in the particulate process has much current interest. This is an important process arising in many engineering disciplines. In this work, the existence of continuous solution of the pure collisional breakage model is developed beneath some restricti...

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Bibliographic Details
Published in:Mathematical methods in the applied sciences 2018-05, Vol.41 (7), p.2715-2732
Main Authors: Paul, Jayanta, Kumar, Jitendra
Format: Article
Language:English
Subjects:
Arzelà‐Ascoli
Breakage
collision
contraction
existence‐uniqueness
Uniqueness
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Summary:The study of collision‐induced breakage phenomenon in the particulate process has much current interest. This is an important process arising in many engineering disciplines. In this work, the existence of continuous solution of the pure collisional breakage model is developed beneath some restrictions on the breakage kernels. Furthermore, the mass conservation and uniqueness of solution are investigated in the absence of “shattering transition.” The underlying theory is based on the compactness result of Arzelà‐Ascoli and Banach contraction mapping principle.
ISSN:0170-4214
1099-1476
DOI:10.1002/mma.4775