Unformatted text preview: itial condition u(x, 0) = cos x.
9. Solve the initial value problem
3 y 2 ux
on the domain x 2xuy = x, u(0, y ) = y
2 0. Hint: In the course notes it is suggested that we should let ⇠ = x, and follow a
standard procedure to ﬁnd an appropriate expression for ⌘ . In this problem it’s
much easier to reverse this; let ⌘ = y , and use the more complicated expression
for ⇠ .
BONUS: If the domain were given instead as y 0, and the initial condition were
given as u (x, 0) = f (x), we would not necessarily be able to solve the
problem (consider, for example, trying to solve this with u (x, 0) = x).
Explain why. Are there any functions f (x) for which a solution would
exist?...
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 Fall '12
 DavidHamsworth
 Boundary value problem, general solution

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