Networks and Heterogeneous Media (NHM)

Biological and industrial models motivating nonlocal conservation laws: A review of analytic and numerical results

Pages: 49 - 67, Volume 11, Issue 1, March 2016      doi:10.3934/nhm.2016.11.49

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Rinaldo M. Colombo - Unità INdAM, c/o DII, Università degli Studi di Brescia, Via Branze, 38; 25123 Brescia, Italy (email)
Francesca Marcellini - Dipartimento di Matematica e Applicazioni, Università di Milano Bicocca, via R. Cozzi 55, 20125 Milano, Italy (email)
Elena Rossi - Dip. di Matematica e Applicazioni, Università di Milano - Bicocca, Via Cozzi, 55; 20125 Milano, Italy (email)

Abstract: This paper is devoted to the overview of recent results concerning nonlocal systems of conservation laws. First, we present a predator -- prey model and, second, a model for the laser cutting of metals. In both cases, these equations lead to interesting pattern formation.

Keywords:  Nonlocal conservation laws, parabolic-hyperbolic problems, laser cutting modeling, predatory -- prey systems.
Mathematics Subject Classification:  Primary: 35L65; Secondary: 35M30, 92D25.

Received: April 2015;      Revised: September 2015;      Available Online: January 2016.