Extending the work of Wollkind, Sriranganathan and Oulton, we study the stability of periodic hexagonal cellular front patterns against small modulations of the periodic structure. For this purpose, we first write down the "amplitude equations" describing the slow space and time variations of the front deformation close to the Mullins-Sekerka bifurcation. We then study the stability of their stationary hexagonal solutions against phase diffusion. We find that, due to phase diffusion instabilities, the range of stability of these solutions is always smaller than their range of existence. © 1984.
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