# First Order Nonlinear Partial Differential Equation

1. Dec 6, 2011

### Compressible

I have derived a first order nonlinear PDE with its corresponding initial and boundary conditions given by:

dv/dt + A*(v^2)*dv/dx = 0 (where A is a constant)

v(t = 0) = C (constant value)
v(x = 0) = 0

I'm not quite sure how to solve this. I was thinking about using the method of characteristics, but since I haven't had too much experience with it, I'm not sure if it would be applicable here. If anyone has any hint on how to get started, I would really appreciate it. Thanks in advance.

2. Dec 6, 2011

### epenguin

I have no experience either but to get started what I would do is write that

$$\frac{∂v}{∂t}/\frac{∂v}{∂x} = -Av^2$$

Then at constant v

$$( \frac{dx}{dy})_v = Av^2$$

$$x = Av^2t + K$$ at constant v.

Fitting that to your initial conditions generates your surface I think. :uhh: Something like that.

3. Dec 7, 2011

### Compressible

Solved! Thanks!

4. Dec 7, 2011

### epenguin

They don't count that as non-linear AFAIK though.