Modèle de trafic routier et caractéristiques

\(\dot x = \gamma \, t\) et \(\dot \rho = \beta \; x^2 (1 + 2\, \gamma \, t^2)\)

\(\dot x = \gamma \, t \)et \(\dot \rho = \beta \; x^2\)

\(\dot x = \gamma \, t\) et \(\dot \rho = 0\)

\(\frac{\partial\, }{\partial x} = \frac{\partial \, }{\partial a}\)   et    \(\frac{\partial \,}{\partial t} = \frac{\partial\, }{\partial \tau}- \gamma \, t \,\frac{\partial \, }{\partial a}\)

\(\frac{\partial \, }{\partial a} = \frac{\partial\, }{\partial x}\)   et   \(\frac{\partial\,}{\partial \tau} =\frac{\partial \, }{\partial t}-\gamma \, t \, \frac{\partial\, }{\partial x}\)

\(\frac{\partial\, }{\partial x} = \frac{\partial \, }{\partial a}+ \frac{1}{\gamma \, t} \;\frac{\partial\, }{\partial \tau}\)    et   \(\frac{\partial \, }{\partial t} = \frac{\partial \, }{\partial \tau}\)