Video lectures on Partial Differential Equations

Here is answer to your Question .Complete course of PDE are available there

http://nptel.ac.in/courses.php

These lectures are there in youtube channel 'nptel" but contents and syllabus can be seen from link above

You can find a lecture on Hyperbolic Conservation Laws, given by Constantine Dafermos here.

And here a course on unique continuation and nonlinear dispersive equations, given by Gustavo Ponce.

Khan Academy is very good with teaching Differential Equations. You should check it out:

Khan Academy