How Can I Perform the Inverse Laplace Transformation for U(s,t)?

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Discussion Overview

The discussion revolves around the inverse Laplace transformation of the function U(s,t), specifically in the context of transforming it to u(x,t). Participants explore the implications of the transformation and the nature of U(s,0) as it relates to boundary conditions.

Discussion Character

  • Exploratory, Technical explanation, Debate/contested

Main Points Raised

  • One participant seeks assistance with the inverse transformation of U(s,t) = U(s,0) * exp[s^2*t], questioning whether the inverse transformation exists.
  • Another participant asks for clarification on the form of U(s,0) as a function.
  • A different participant notes that U(s,0) is derived from boundary conditions, specifically mentioning u(x,t=0) = u(x) = delta_dirac(x).
  • Another contribution highlights that while U(s,0) can be fixed, there is a concern regarding a singularity at infinity in the expression.

Areas of Agreement / Disagreement

Participants express uncertainty regarding the existence of the inverse transformation and the implications of the singularity, indicating that multiple views and concerns remain unresolved.

Contextual Notes

There are limitations regarding the assumptions about U(s,0) and the nature of the singularity, which may affect the transformation process.

germana2006
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Help me please with the next Laplace inverse transformation:

U(s,t)=U(s,0)*exp[s^2*t]

Transformation from U(s,t) to u(x,t).
I don't know if this inverse transformation exit or not.

Thank you very much.
 
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How does U(s,0) look like as a function ?

Daniel.
 
U(s,0) come from the boundary conditions, u(x,t=0)=u(x)=deltadirac(x)
 
You can fix U(s,0), but the e hat a singularity in infinity.
 

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