Derive a solution formula for the initial-boundary value problem
ut = Duxx + f(x, t), x 0, t 0,
with initial condition u(x, 0) = (x) and boundary condition ux(0, t) = g(t). [Hint: use
v(x, t) = u(x, t) xg(t) and apply Duhamel’s principle.]

Derive a solution formula for the initial-boundary value problem
ut = Duxx + f(x, t), x 0, t 0,
with initial condition u(x, 0) = (x) and boundary condition ux(0, t) = g(t). [Hint: use
v(x, t) = u(x, t) xg(t) and apply Duhamel’s principle.]