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?
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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 .
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