Duhamel iteration argument: Difference between revisions
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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]]. | 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]]. | ||
[[Category: | [[Category:Methods]] | ||
Latest revision as of 00:12, 18 August 2006
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.
