Mathematical Modeling - Adsorption Column using Duhamel Theorem

[cgf_chem]

Hi all!

I´m trying to understand all the equations of the article in attachment and have many difficulties. Can someone help me to deduce the equation 4 and how I use de Duhamel Theorem to go to the equation 6 for the equation 24?

Thanks for any help here!!!

 

[hacksaw]

The author is going from a solution for a step (Heaviside) change in concentration, to a solution where the concentration evolves over time,

you'll notice the time derivative of u bar in (24)

this is equivalent to converting the step reponse to the "impulse response" to a Dirac delta function.

a commonly used approach,