Solving partial differential equation (use characteristic method) $$\Large \frac{\partial u }{\partial t} + u^2 \frac{\partial u}{\partial x}=0 , 0

Question

Solving partial differential equation (use characteristic method)

$$\Large \frac{\partial u }{\partial t} + u^2 \frac{\partial u}{\partial x}=0 ,  0 < x < \infty , t>0$$
initial value $ \Large u(x,0) = \sqrt{x}, 0< x < \infty$

experimentx · Answer

what's a characteristic method?

chihiroasleaf · Answer

using characteristic equation...

experimentx · Answer

what characteristic equation ... seems like you cross-posted on MSE http://math.stackexchange.com/questions/309117/solve-partial-differential-equation-using-characteristic-method-with-non-zero-ri

experimentx · Answer

so far i've known these DE (first order) can be solved using Lagrange method ... or using variable separation method.

chihiroasleaf · Answer

it's different question of mine... :lol: 

I've just learn this topic so I don't learn other method yet...

experimentx · Answer

looks like you are looking for Lagrange method. unfortunately i lent my book to my friend ... looks like i've to google. do you know how to solve this type of equations? http://upload.wikimedia.org/math/3/0/8/30868ddc9b1fee7e8218e76d22efd1be.png

chihiroasleaf · Answer

no.., I don't know... -_- it's looks like this http://en.wikipedia.org/wiki/Method_of_characteristics#Example

experimentx · Answer

all right ... what's the characteristic equation for it

chihiroasleaf · Answer

I'm not sure that I can explain well about characteristic equation...
but here the characteristic equation will make the PDE becomes ODE..., so we can find the solution of PDE by solving systems of ODE...

experimentx · Answer

yes ... |dw:1361376539931:dw|