Multiclass Lighthill-Whitham-Richards trafficmodels[Benzoni-Gavage and Colombo,Euro.J.Appl.Math.,14(2003),pp.587–612;Wong and Wong,Transp.Res.A,36(2002),pp.827–841]give rise to first-order systems of conservation la...Multiclass Lighthill-Whitham-Richards trafficmodels[Benzoni-Gavage and Colombo,Euro.J.Appl.Math.,14(2003),pp.587–612;Wong and Wong,Transp.Res.A,36(2002),pp.827–841]give rise to first-order systems of conservation laws that are hyperbolic under usual conditions,so that their associated Cauchy problems are wellposed.Anticipation lengths and reaction times can be incorporated into these models by adding certain conservative second-order terms to these first-order conservation laws.These terms can be diffusive under certain circumstances,thus,in principle,ensuring the stability of the solutions.The purpose of this paper is to analyze the stability of these diffusively correctedmodels under varying reaction times and anticipation lengths.It is demonstrated that instabilities may develop for high reaction times and short anticipation lengths,and that these instabilities may have controlled frequencies and amplitudes due to their nonlinear nature.展开更多
基金R.Burger acknowledges partial support by Fondecyt project 1130154BASAL project CMM,U.de Chile and Centro de Investigacion en Ingenierıa Matematica(CI2MA),U.de Concepcion+1 种基金Conicyt project Anillo ACT1118(ANANUM)and Red Doctoral REDOC.CTA,MINEDUC project UCO1202 at U.de Concepcion.P.Mulet is partially supported by Spanish MCINN MTM2011-22741.L.M.Villada is supported by MECESUP project UCO0713.
文摘Multiclass Lighthill-Whitham-Richards trafficmodels[Benzoni-Gavage and Colombo,Euro.J.Appl.Math.,14(2003),pp.587–612;Wong and Wong,Transp.Res.A,36(2002),pp.827–841]give rise to first-order systems of conservation laws that are hyperbolic under usual conditions,so that their associated Cauchy problems are wellposed.Anticipation lengths and reaction times can be incorporated into these models by adding certain conservative second-order terms to these first-order conservation laws.These terms can be diffusive under certain circumstances,thus,in principle,ensuring the stability of the solutions.The purpose of this paper is to analyze the stability of these diffusively correctedmodels under varying reaction times and anticipation lengths.It is demonstrated that instabilities may develop for high reaction times and short anticipation lengths,and that these instabilities may have controlled frequencies and amplitudes due to their nonlinear nature.
