scholarly journals Global solution to the Cauchy problem for discrete velocity models of vehicular traffic

2012 ◽  
Vol 252 (2) ◽  
pp. 1350-1368 ◽  
Author(s):  
N. Bellomo ◽  
A. Bellouquid
Keyword(s):  
Cauchy Problem ◽  
Global Solution ◽  
Vehicular Traffic ◽  
Discrete Velocity Models ◽  
Discrete Velocity ◽  
Velocity Models ◽  
The Cauchy Problem

scholarly journals Enskog-like discrete velocity models for vehicular traffic flow

2007 ◽  
Vol 2 (3) ◽  
pp. 481-496 ◽  
Author(s):  
Michael Herty ◽  
◽  
Lorenzo Pareschi ◽  
Mohammed Seaïd ◽  
◽  
...  
Keyword(s):  
Traffic Flow ◽  
Vehicular Traffic ◽  
Discrete Velocity Models ◽  
Discrete Velocity ◽  
Velocity Models ◽  
Vehicular Traffic Flow

LIMIT THEOREMS FOR DETERMINISTIC KNUDSEN FLOWS BETWEEN TWO PLATES

1996 ◽  
Vol 06 (04) ◽  
pp. 503-520 ◽  
Author(s):  
HANS BABOVSKY
Keyword(s):  
Large Class ◽  
Test Particle ◽  
Limit Theorems ◽  
Velocity Model ◽  
Diffusion Limit ◽  
Parallel Plates ◽  
Discrete Velocity Models ◽  
Discrete Velocity ◽  
Velocity Models ◽  
Model Dynamics

We investigate the model dynamics of a test particle which moves between two parallel plates and is reflected at the walls according to some deterministic periodic reflection law. For a particular continuous velocity model, a diffusion limit is derived using the Markov partition approach. It is shown that at least for a large class of discrete velocity models such a limit is not possible. Numerical aspects are discussed.

The critical exponents of parabolic equations and blow-up in Rn

1998 ◽  
Vol 128 (1) ◽  
pp. 123-136 ◽  
Author(s):  
Yuan-wei Qi
Keyword(s):  
Cauchy Problem ◽  
Global Solution ◽  
Nontrivial Solution ◽  
Critical Exponents ◽  
Parabolic Equations ◽  
Finite Time ◽  
Blow Up ◽  
Initial Value ◽  
The Cauchy Problem

In this paper we study the Cauchy problem in Rn of general parabolic equations which take the form ut = Δum + ts|x|σup with non-negative initial value. Here s ≧ 0, m > (n − 2)+/n, p > max (1, m) and σ > − 1 if n = 1 or σ > − 2 if n ≧ 2. We prove, among other things, that for p ≦ pc, where pc ≡ m + s(m − 1) + (2 + 2s + σ)/n > 1, every nontrivial solution blows up in finite time. But for p > pc a positive global solution exists.

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