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

Rinaldo M.  Colombo; Francesca  Marcellini; Elena  Rossi

doi:10.3934/nhm.2016.11.49

Article Contents

2016, Volume 11, Issue 1: 49-67. Doi: 10.3934/nhm.2016.11.49

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

1.
Unità INdAM, c/o DII, Università degli Studi di Brescia, Via Branze, 38; 25123 Brescia
2.
Dip. di Matematica e Applicazioni, Università di Milano - Bicocca, Via Cozzi, 55; 20125 Milano

Received: March 31, 2015

Revised: August 31, 2015

Published: February 2016

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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.

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Mathematics Subject Classification: Primary: 35L65; Secondary: 35M30, 92D25.

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