NonLocal Systems of Balance Laws in Several Space Dimensions with Applications to Laser Technolog

TL;DR

This paper proves local existence and continuous dependence of solutions for a class of nonlinear, nonlocal balance laws in multiple dimensions, motivated by laser cutting and conveyor belt models, with numerical results aligning with real-world phenomena.

Contribution

It introduces a new class of nonlocal balance law systems, proving their well-posedness and applying them to laser cutting and particle conveyor models with realistic simulations.

Findings

Numerical solutions match qualitative properties of laser cuts.

Models accurately describe metal cutting and particle dynamics.

Theoretical results ensure stability and dependence on initial data.

Abstract

For a class of systems of nonlinear and nonlocal balance laws in several space dimensions, we prove the local in time existence of solutions and their continuous dependence on the initial datum. The choice of this class is motivated by a new model devoted to the description of a metal plate being cut by a laser beam. Using realistic parameters, solutions to this model obtained through numerical integrations meet qualitative properties of real cuts. Moreover, the class of equations considered comprises a model describing the dynamics of solid particles along a conveyor belt.