Thread: Advection Equation

Solve:

ut + ((x-1)u)x=0, x E(0,1) & t > 0

I want to try the solution u(x,t) = f(x + ct), but think this might be incorrect, any ideas?

By the way ut, means differnatiate u with t, and ((x-1)u) is differentiated by x

Originally Posted by ryanhorne

Solve:

ut + ((x-1)u)x=0, x E(0,1) & t > 0

I want to try the solution u(x,t) = f(x + ct), but think this might be incorrect, any ideas?

If you directly substitute your solution form into the PDE you'll get



If you let this becomes



Now differentiate wrt gives . So the only form is constant.

The actual solution of the PDE is .

You a Genius! Cheers