andrey21
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A model for single land of traffic is given below:
p.dv/dx + v. dp/dx + dp/dt = 0
Where v = kx/p
Show that with the expression for p, the PDE becomes:
dp/dt = -k
Here is my attempt
v = kx/p
dv/dx = k/p
Sub into pde:
p (k/p) + (kx/p) .dp/dx + dp/dt = 0
k + (kx/p). dp/dx + dp/dt = 0
This is how far I can get, any help would be great.
p.dv/dx + v. dp/dx + dp/dt = 0
Where v = kx/p
Show that with the expression for p, the PDE becomes:
dp/dt = -k
Here is my attempt
v = kx/p
dv/dx = k/p
Sub into pde:
p (k/p) + (kx/p) .dp/dx + dp/dt = 0
k + (kx/p). dp/dx + dp/dt = 0
This is how far I can get, any help would be great.