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.

Colombo, R., Marcellini, F. (2015). NonLocal Systems of Balance Laws in Several Space Dimensions with Applications to Laser Technology. JOURNAL OF DIFFERENTIAL EQUATIONS, 259(11), 6749-6773 [10.1016/j.jde.2015.08.005].

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

MARCELLINI, FRANCESCA
2015

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.
Articolo in rivista - Articolo scientifico
Nonlocal balance laws; Laser cutting; Conveyor belt dynamics
English
ago-2015
2015
259
11
6749
6773
7966
none
Colombo, R., Marcellini, F. (2015). NonLocal Systems of Balance Laws in Several Space Dimensions with Applications to Laser Technology. JOURNAL OF DIFFERENTIAL EQUATIONS, 259(11), 6749-6773 [10.1016/j.jde.2015.08.005].
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Utilizza questo identificativo per citare o creare un link a questo documento: https://hdl.handle.net/10281/99511
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