  We model pacemaker effects of an algebraically localized heterogeneity in a 1
dimensional array of oscillators with nonlocal coupling. We assume the
oscillators obey simple phase dynamics and that the array is large enough so
that it can be approximated by a continuous nonlocal evolution equation. We
concentrate on the case of heterogeneities with positive average and show that
steady solutions to the nonlocal problem exist. In particular, we show that
these heterogeneities act as a wave source, sending out waves in the far field.
This effect is not possible in 3 dimensional systems, such as the complex
Ginzburg-Landau equation, where the wavenumber of weak sources decays at
infinity. To obtain our results we use a series of isomorphisms to relate the
nonlocal problem to the viscous eikonal equation. We then use Fredholm
properties of the Laplace operator in Kondratiev spaces to obtain solutions to
the eikonal equation, and by extension to the nonlocal problem.
