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I am having trouble understanding how to use Duhamel's formula as a contraction to give existence uniqueness theorems for certain semi linear PDE.

To be more precise, have a look at the PDE and corresponding Duhamel formula in the wikipedia link given below:

http://tosio.math.toronto.edu/wiki/index.php/Duhamel's_formula

How is the exp(tL) even rigorously, defined? I can't find this anywhere.

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# Duhamel's formula and iterates.

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