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## Homework Statement

Solve

[tex] \frac{\partial{w}}{\partial{t}} + c \frac{\partial{w}}{\partial{x}} =0 \hspace{3 mm} (c>0) [/tex]

for x>0 and t>0 if

[tex] w(x,0) = f(x) [/tex]

[tex] w(0,t) = h(t) [/tex]

## Homework Equations

## The Attempt at a Solution

I know how to solve for the conditions separately and that would give

[tex] w(x,t) = f(x-ct) [/tex] and

[tex] w(x,t) = h(t-\frac{1}{c}x) [/tex]

but how do you solve it for both? And when does x>0 or t>0 matter?

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