Global Solutions to the Discrete Nonlinear Breakage Equations without Mass Transfer

TL;DR

This paper proves the global existence, uniqueness, and large-time behavior of solutions to discrete nonlinear breakage equations, supported by numerical simulations, without requiring growth assumptions on collision kernels.

Contribution

It establishes the first comprehensive analysis of global solutions to discrete nonlinear breakage equations without growth restrictions on collision kernels.

Findings

Global existence of solutions is proven for broad collision kernels.

Classical solutions are constructed and shown to be unique.

Numerical simulations support the theoretical results.

Abstract

Global existence of mild solutions to the discrete collisional breakage equations is established for a broad class of collision kernels, without imposing any growth assumptions. In addition, classical solutions are constructed, and uniqueness is proved for an appropriate class of kinetic coefficients and initial data. The large time behavior of solutions is also discussed, and numerical simulations are presented to support the theoretical results.