Mass-Conserving Self-Similar Solutions to Collision-Induced Breakage Equations

2024/05/10 by Jaiswal, Ram Gopal, Giri, Ankik Kumar
#35B40 #35C06 #35D30 #37C25 #45K05 #Analysis of PDEs (math.AP) #FOS: Mathematics

paper · doi:10.48550/arxiv.2405.06757

Abstract

Existence of mass-conserving self-similar solutions to collision-induced breakage equation is shown for a specific class of homogeneous collision kernels and breakage functions. The proof mainly relies on a dynamical approach and compactness method to constructing mass-conserving stationary solutions for an evolution problem, which induces mass-conserving self-similar solutions to collision-induced breakage equation. Furthermore, we also determine lower and upper bound of the scaling profile.

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