Mathematics, 02.01.2020 21:31 mikayla62

Find u(t, x) solving the ivp on the half-line for the diffusion equation:

ut - uxx = 0 (t> 0; x in r)
ux(t,0) = sin(t)
u(0,x) = x

i can do this problem for the most part but i'm struggling to get rid of the non-zero neumann boundary condition. (i know the heat kernel/fundamental solution and odd/even reflection technique).

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Find u(t, x) solving the ivp on the half-line for the diffusion equation:

ut - uxx = 0...