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    Derive Source Solution by Performing Integral Tranforms on a Heat Equation.

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    Derive the source solution by performing integral transforms of the equation:

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    Problem.

    Derive the source solution by performing integral transforms of the equation:

    Solution:

    Let's consider the general homogenous Cauchy problem of heat equation:
    ( 1)
    with initial condition:
    ( 2)
    There best method to determine the solution of (1) + (2) consists in using the integral transforms (Laplace and Fourier).

    We will use the following definitions and integral transforms:

    1) (x) = Dirac distribution (sometimes called "Dirac impulse function") which satisfies the equation
    ( 3)
    2) The "convolution product" between 2 functions (or distributions) is defined as
    for 0 < t <  ( 4)
    or
    for x  R ( 5)
    3) The Laplace transform:
    ( 6)
    4) Laplace transform ...

    Solution Summary

    The Source Solution is derived by Performing Integral Tranforms on a Heat Equation. The solution is detailed and well presented.

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