# Existence and uniqueness of PDEs

1. Sep 7, 2011

### daniel_8775

Hello,

I have a PDE:

3*u_x + 2*u_y = 0, and I am interested in determining initial values such that there is a unique solution, there are multiple solutions, and there are no solutions at all.

What theorem(s)/techniques would be of use to me for something like this?

Regards,
Dan

2. Sep 8, 2011

### hunt_mat

You should be thinking of the method of characteristics.

The general solution to your equation is $u=f(2x-3y)$