Acta mathematica scientia, Series B >
NONLOCAL CROWD DYNAMICS MODELS FOR SEVERAL POPULATIONS
Received date: 2011-10-16
Online published: 2012-01-20
Supported by
The second author was partially supported by the GNAMPA 2011 project Non Standard Applications of Conservation Laws.
This paper develops the basic analytical theory related to some recently intro-duced crowd dynamics models. Where well posedness was known only locally in time, it is here extended to all of R+ . The results on the stability with respect to the equations are improved. Moreover, here the case of several populations is considered, obtaining the well posedness of systems of multi-D non-local conservation laws. The basic analytical tools are provided by the classical Kruˇzkov theory of scalar conservation laws in several space dimensions.
Key words： hyperbolic conservation laws; nonlocal flow; pedestrian traffic
Rinaldo M. Colombo , Magali L′ecureux-Mercier . NONLOCAL CROWD DYNAMICS MODELS FOR SEVERAL POPULATIONS[J]. Acta mathematica scientia, Series B, 2012 , 32(1) : 177 -196 . DOI: 10.1016/S0252-9602(12)60011-3
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