Inverse Laplace Transform of a product of exponential functions

  • Thread starter metdave
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  • #1
metdave
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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?

Thanks!
David
 

Answers and Replies

  • #2
JJacquelin
801
34
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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