  In an appropriate moving coordinate frame, source defects are time-periodic
solutions to reaction-diffusion equations that are spatially asymptotic to
spatially periodic wave trains whose group velocities point away from the core
of the defect. In this paper, we rigorously establish nonlinear stability of
spectrally stable source defects in the complex Ginzburg-Landau equation. Due
to the outward transport at the far field, localized perturbations may lead to
a highly non-localized response even on the linear level. To overcome this, we
first investigate in detail the dynamics of the solution to the linearized
equation. This allows us to determine an approximate solution that satisfies
the full equation up to and including quadratic terms in the nonlinearity. This
approximation utilizes the fact that the non-localized phase response,
resulting from the embedded zero eigenvalues, can be captured, to leading
order, by the nonlinear Burgers equation. The analysis is completed by
obtaining detailed estimates for the resolvent kernel and pointwise estimates
for the Green's function, which allow one to close a nonlinear iteration
scheme.
