Solve the following initial value problem for u(x, ) on a semi-infinite interval, using a Greens

Solve the following initial value problem for u(x, τ ) on a semi-infinite interval, using a Green’s function:

with
u(x, 0) = u₀(x) for x > 0, u(0, τ ) = 0 for τ > 0.

Define v(x, τ) as

v(x, τ ) = u(x, τ) if x > 0,
v(x, τ ) = −u(−x, τ) if x < 0.

Then we can show that v(0, τ ) = 0 and

Transcribed Image Text:

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