Corso di Dottorato

"Flussi di traffico su reti"

Docente: Benedetto Piccoli

 

Orario (indicativo):   Lunedi e Giovedě dalle 10:00 alle  11:30.  Inizio Lunedě 1 Dicembre 2008 ore 10:00.

Sede:  Istituto per le Applicazioni del Calcolo "M. Picone", Viale del Policlinico 137, 00161 Roma

Argomenti del corso:
 

Basics of conservation laws: classical solutions, gradient’s blow up, weak solutions and entropy solutions, existence by wave front tracking, uniqueness by tangent vectors.

Car traffic models by partial differential equations: Lighthill-Whitham-Richards model, Aw-Rascle second order model, Colombo phase transition model.

Networks: general definitions, Riemann solvers at junctions, bound on waves and interactions; LWR on networks, other models on networks; data networks; supply chains;

Numerics for conservation laws on networks.

 

 
Bibliografia: 

 

Leggi di conservazione:

A. Bressan, Hyperbolic Systems of Conservation Laws, Oxford, 2000.

C. Dafermos, Hyperbolic Conservation Laws in Continuum Physics, Springer-Verlag, 1999.

 

H. Holden, N.H. Risebro, Front tracking for hyperbolic conservation laws, Springer, 2002.

 

D. Serre, Systems of conservation laws I and II, Diderot Editeur, 1996.

Traffico su reti:

M. Garavello, B. Piccoli, Traffic flow on networks, American Institute of Mathematical Sciences, 2006.