Mathematical Biosciences and Engineering (MBE)

On the initial value problem for a class of discrete velocity models
Pages: 31 - 43, Issue 1, February 2017

doi:10.3934/mbe.2017003      Abstract        References        Full text (419.1K)           Related Articles

Davide Bellandi - University of Ferrara, Department of Mathematics and Computer Science, Via Machiavelli 35, 44121 Ferrara, Italy (email)

1 G. Ajmone Marsan, N. Bellomo and A. Tosin, Complex Systems and Society: Modeling and Simulation, Springer, 2013.       
2 L. Arlotti, E. De Angelis, L. Fermo, M. Lachowicz and N. Bellomo, On a class of integro-differential equations modeling complex systems with nonlinear interactions, Appl.Math. Lett. 25 (2012), 490-495.       
3 N. Bellomo and A. Bellouquid, Global solution to the Cauchy problem for discrete velocity models of vehicular traffic, J. Differ. Equations, 252 (2012), 1350-1368.       
4 N. Bellomo, V. Coscia and M. Delitala, On the mathematical theory of vehicular traffic fow I - Fluid dynamic and kinetic modeling, Math. Mod. Meth. Appl. Sci., 12 (2002), 1801-1843.       
5 N. Bellomo and C. DogbĂ©, On the modelling of traffic and crowds - a survey of models, speculations and perspectives, SIAM Rev., 53 (2011), 409-463.       
6 N. Bellomo, D. Knopoff and J. Soler, On the difficult interplay between life, "complexity", and mathematical sciences, Math. Mod. Meth. Appl. Sci. 23 (2013), 1861-1913.       
7 N. Bellomo, B. Piccoli and A. Tosin, Modeling crowd dynamics from a complex system viewpoint, Math. Mod. Meth. Appl. Sci., 22 (2012), 1230004, 29pp.       
8 A. Bellouquid, E. De Angelis and L. Fermo, Towards the modeling of vehicular traffic as a complex system: A kinetic theory approach, Math. Mod. Meth. Appl. Sci., 22 (2012), 1140003, 35pp.       
9 A. Bellouquid and M. Delitala, Mathematical Modeling of Complex Biological Systems. A Kinetic Theory Approach, Birkhäuser, Boston, 2006.       
10 A. Benfenati and V. Coscia, Nonlinear microscale interactions in the kinetic theory of active particles, Appl. Math. Lett., 26 (2013), 979-983.       
11 V. Coscia, M. Delitala and P. Frasca, On the mathematical theory of vehicular traffic flow II: Discrete velocity kinetic models, Int. J. Non-Linear Mech., 42 (2007), 411-421.       
12 V. Coscia, L. Fermo and N. Bellomo, On the mathematical theory of living systems II: The interplay between mathematics and system biology, Comput. Math. Appl., 62 (2011), 3902-3911.       
13 M. Delitala and A. Tosin, Mathematical modeling of vehicular traffic: A discrete kinetic theory approach, Math. Mod. Meth. Appl. Sci., 17 (2007), 901-932.       
14 L. Arlotti, N. Bellomo, E. De Angelis and M. Lachowicz, Generalized Kinetic Models in Applied Sciences, World Scientific, New Jersey, 2003.       
15 J. Banasiak and M. Lachowicz Methods of Small Parameter in Mathematical Biology, Birkhauser, 2014.       
16 S. Kaniel and M. Shinbrot, The Boltzmann equation. I. Uniqueness and local existence, Math. Phys., 58 (1978), 65-84.       
17 B. S. Kerner, The Physics of Traffic, Empirical Freeway Pattern Features, Engineering Applications and Theory, Springer, 2004.
18 P. Lax, Hyperbolic Partial Differential Equations, Courant Lecture Notes, 2006.       

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