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The heat is both diffusing and advecting in a 1-d domain [0, 1]. The temperature satisfies...

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Physics

The heat is both diffusing and advecting in a 1-d domain [0, 1].The temperature satisfies the equation ut = Duxx − cux − λu, 0 0, u(0, t) = 1, u(1, t) = 1, t > 0, u(x, 0) =u0(x), 0 ≤ x ≤ 1. (a) Determine whether there exists a steadystate. Find the steady state if it exists. (b) When the steadystate exists, graph the steady-state temperature distribution inthe interval and analyze how heat is flowing in the interval andthrough its boundaries. You may pick specific values for thegraph.

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