An existence‐uniqueness result for the pure binary collisional breakage equation. (19th February 2018)

• Record Type: Journal Article
• Authors: Paul, Jayanta; Kumar, Jitendra
• Is Part Of: Mathematical methods in the applied sciences. Volume 41:Number 7(2018)
• Page Start: 2715
• Page End: 2732
• Publication Date: 2018-02-19
• Subjects: Arzelà‐Ascoli -- breakage -- collision -- contraction -- existence‐uniqueness; Mathematics -- Periodicals; Technology -- Mathematics -- Periodicals; 519
• DOI: 10.1002/mma.4775
• Languages: English
• ISSNs: 0170-4214

Abstract

Abstract : 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.