The heat flux of a solution u(x, t) across x = 0 is defined by (t) =

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The heat flux of a solution u(x, t) across x = 0 is defined by Φ(t) = -Kux(0, t). Find Φ(t) for the solution (9). Explain the name. Is it physically understandable that Φ goes to 0 as t → ∞?

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