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3. Solve the Neumann problem for diffusion on the half-line: ut − kuxx = 0 subject...

3. Solve the Neumann problem for diffusion on the half-line: ut − kuxx = 0 subject to u(x, 0) = φ(x), x > 0, ux(0, t) = 0, t > 0. Use an appropriate extension of the initial data to the whole real line and simplify the expression for u(x, t) so that the domain of the integral is [0, ∞). (See the notes for a similar formula for the Dirichlet problem.)

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