Existence and uniqueness of PDEs

[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

[hunt_mat]

You should be thinking of the method of characteristics.

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