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Inverse Laplace Transform of a product of exponential functions

  1. Aug 28, 2013 #1
    I am reviewing some material on Laplace Transforms, specifically in the context of solving PDEs, and have a question.

    Suppose I have an Inverse Laplace Transform of the form u(s,t)=e^((as^2+bs)t) where a,b<0. How can I invert this with respect to s, giving a function u(x,t)? Would the inverse transform simply be a convolution?

  2. jcsd
  3. Aug 29, 2013 #2
    Hi !
    I fear that this may not be possible.
    Try to find the Inverse Laplace transform of exp(-s²) for example.
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