Developments in the theory of the PrigogineHerman kinetic equation of vehicular traffic
(2000) Abstract
 The nonlinear kinetic equation of Prigogine and Herman is examined in regards to existence and uniqueness of solutions. The solution exists and is unique in the Banach space of bounded continuous functions over a particular subspace Ω.
The equilibrium solution of the kinetic equation of Prigogine and Herman is used to derive asymptotic type series expansions in the form of Hilbert or Chapman and Enskog for concentrations (c ) corresponding to the stable flow regime of traffic (0 < c < c crit ). As expected the conservation of mass equation, the LighthillWhithamRichards model, can be obtained from these expansions.
We use the ChapmanEnskog expansion to obtain hydrodynamiclike equations... (More)  The nonlinear kinetic equation of Prigogine and Herman is examined in regards to existence and uniqueness of solutions. The solution exists and is unique in the Banach space of bounded continuous functions over a particular subspace Ω.
The equilibrium solution of the kinetic equation of Prigogine and Herman is used to derive asymptotic type series expansions in the form of Hilbert or Chapman and Enskog for concentrations (c ) corresponding to the stable flow regime of traffic (0 < c < c crit ). As expected the conservation of mass equation, the LighthillWhithamRichards model, can be obtained from these expansions.
We use the ChapmanEnskog expansion to obtain hydrodynamiclike equations equivalent to the Euler, NavierStokes or Burnett equations of fluid flow, depending on the order of the series expansions we used. The zeroth and first order hydrodynamiclike partial differential equations are solved using appropriate conservative numerical schemes. Analogous continuum approximations up to order one are obtained from the Hilbert expansion.
Last a zerothorder (extended LighthillWhithamRichards) model is obtained for unstable flow at sufficiently high concentrations. (Less)
Please use this url to cite or link to this publication:
http://lup.lub.lu.se/record/2201872
 author
 Sopasakis, Alexandros ^{LU}
 opponent

 Prabir, Daripa, Mathematics, Texas A&M University
 organization
 publishing date
 2000
 type
 Thesis
 publication status
 published
 subject
 keywords
 ChapmanEnskog expansion, Traffic, PrigogineHerman, Kinetic equation, Unstable flow
 pages
 112 pages
 defense location
 College Station, Texas, USA
 defense date
 20000526 10:00
 ISBN
 0599738111
 9780599738119
 language
 English
 LU publication?
 yes
 id
 92f33e0a748a4d719e4321a4edd5e46d (old id 2201872)
 date added to LUP
 20160314 14:42:00
 date last changed
 20170209 12:04:32
@phdthesis{92f33e0a748a4d719e4321a4edd5e46d, abstract = {The nonlinear kinetic equation of Prigogine and Herman is examined in regards to existence and uniqueness of solutions. The solution exists and is unique in the Banach space of bounded continuous functions over a particular subspace Ω.<br/><br> <br/><br> The equilibrium solution of the kinetic equation of Prigogine and Herman is used to derive asymptotic type series expansions in the form of Hilbert or Chapman and Enskog for concentrations (c ) corresponding to the stable flow regime of traffic (0 < c < c crit ). As expected the conservation of mass equation, the LighthillWhithamRichards model, can be obtained from these expansions.<br/><br> <br/><br> We use the ChapmanEnskog expansion to obtain hydrodynamiclike equations equivalent to the Euler, NavierStokes or Burnett equations of fluid flow, depending on the order of the series expansions we used. The zeroth and first order hydrodynamiclike partial differential equations are solved using appropriate conservative numerical schemes. Analogous continuum approximations up to order one are obtained from the Hilbert expansion.<br/><br> <br/><br> Last a zerothorder (extended LighthillWhithamRichards) model is obtained for unstable flow at sufficiently high concentrations.}, author = {Sopasakis, Alexandros}, isbn = {0599738111}, keyword = {ChapmanEnskog expansion,Traffic,PrigogineHerman,Kinetic equation,Unstable flow}, language = {eng}, pages = {112}, school = {Lund University}, title = {Developments in the theory of the PrigogineHerman kinetic equation of vehicular traffic}, year = {2000}, }