The equation is ut + uux + uxxx = 0
I need to show that this is a parabolic pde.
Hint : convert to an equivalent system of 1st order equations by introducing an auxiliary variable p = ux, etc.
The Attempt at a Solution
So i took p = ux
doesn't that just give me:
ut + pu + pxx = 0
This i think is a parabolic pde by inspection.
But the hint says i need to get a system of 1st order equations. What am i missing? I am pretty sure I've made a giant error. Help please!