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

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

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genius_generous answered 2 years ago

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