The saline concentration u in a thin metal tube of length 1 containing the solution satisfies the diffusion equation Ju

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The Saline Concentration U In A Thin Metal Tube Of Length 1 Containing The Solution Satisfies The Diffusion Equation Ju 1 (76.95 KiB) Viewed 35 times

The saline concentration u in a thin metal tube of length 1 containing the solution satisfies the diffusion equation Ju ² u 0 < x < 1, t> 0. Ət მე2 (Note that the diffusion constant is not 1 in this problem.) - 0 at the boundary. Thus the initial and boundary ах Assume flux of saline at the boundary is zero, that is, assume conditions in this situation are du Ju -(0, t) = (1,t) = 0, t> 0 əx əx u (x, 0) = x, 0 < x < 1 Use separation of variables to look for solutions of the form v (x) w (t). Use the diffusion constant 2 only in finding w (t). Determine a basis of normalized functions (amplitude 1) that spans the space of possible solutions uk (x, t) = vk (x) wk (t). uk (x, t) = vk (x) wk (t) = 2 "