Consider du = kou au. This corresponds to a one-dimensional rod either with heat loss through...

 

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Consider du = kou au. This corresponds to a one-dimensional rod either with heat loss through the lateral sides with outside temperature 0(a > 0) or with insulated lateral sides with a heat sink proportional to the temperature. Suppose that the boundary conditions are u(0, t) = 0 and u(L, t) = 0. a) What are the possible equilibrium temperature distributions is a > 0? b) Solve the time-dependent problem [u(x, 0) = f(x)] if a > 0. Analyze the temperature for large time (t → ∞) and compare to part (a). Consider du = kou au. This corresponds to a one-dimensional rod either with heat loss through the lateral sides with outside temperature 0(a > 0) or with insulated lateral sides with a heat sink proportional to the temperature. Suppose that the boundary conditions are u(0, t) = 0 and u(L, t) = 0. a) What are the possible equilibrium temperature distributions is a > 0? b) Solve the time-dependent problem [u(x, 0) = f(x)] if a > 0. Analyze the temperature for large time (t → ∞) and compare to part (a).

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The image contains a mathematical problem involving a partial differential equation that models heat conduction in a rod with heat loss alongside some ... View the full answer