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    Heat Equation Problem

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    Find the solution u(x,t) of the heat equation:
    ut = 1/2 uxx

    (a) with initial data u(x,0) = x
    (b) with initial data u(x,0) = x^2
    (c) with initial data u(x,0) = sinx
    (d) with initial data u(x,0) = 0 x < 0 and u(x,0) = 1 or x >/= 0

    I know the solution of the heat equation with given initial data is unique. So if you happen to guess a function that satisfies the heat equation and satisfies initial condition, then it is a unique solution.

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    Solution Summary

    Heat equation problem is assessed in the solution.