Duhamel's principle states that the solution of an inhomogeneous linear evolution equation is a superposition of solutions of the corresponding homogeneous equation.
If 
is the solution operator for 
and 
, then the solution of 
is formally
 |
The integrand propagates the forcing introduced at time 
through the remaining time 
.
For an ordinary differential equation or a linear time-invariant system, this representation becomes the Duhamel integral. For the inhomogeneous wave equation, it expresses the solution as an integral of solutions generated by instantaneous source data.
