# Duhamel iteration argument

From DispersiveWiki

The **Duhamel iteration argument** is a means of constructing solutions to a Cauchy problem by recasting these solutions (via Duhamel's formula) as a fixed point of a nonlinear map. One then finds a function space for which this map is a contraction, at which point the solution is guaranteed to exist from the contraction mapping theorem.

This argument is particularly well suited to semilinear equations (both with and without derivatives in the nonlinearity), as it tends to imply very strong versions of wellposedness.