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Derive the source solution by performing integral transforms of the equation:© BrainMass Inc. brainmass.com December 24, 2021, 5:10 pm ad1c9bdddf
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Derive the source solution by performing integral transforms of the equation:
Let's consider the general homogenous Cauchy problem of heat equation:
with initial condition:
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
2) The "convolution product" between 2 functions (or distributions) is defined as
for 0 < t < ( 4)
for x R ( 5)
3) The Laplace transform:
4) Laplace transform ...
The Source Solution is derived by Performing Integral Tranforms on a Heat Equation. The solution is detailed and well presented.