If there is a heat transfer from the lateral surface of a thin wire of length L into a medium at constant temperature um, then the heat equation takes on the form k 02 u 0x2 2 h(u 2 um) 0u 0t , 0 , x , L, t . 0, where h is a constant. Find the temperature u(x, t) if the initial temperature is a constant u0 throughout and the ends x 0 and x L are insulated.

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