# Deriving of Duhamel Theorem

Deriving of Duhamel-theorem will be executed in the followings.

Let’s start from the weak derivative of convolution

Apply the following denoting:

Let’s describe the convolution formula in the argument of weak derivative:

If , and
, where
Now, it is possible to get the final expression of Duhamel-theorem
, where means the conventional derivative, which is denoted by “” as usual.