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Math. Anal."],"published-print":{"date-parts":[[2018,1]]},"abstract":"<jats:p>We study the planar front solution for a class of reaction diffusion equations in multidimensional space in the case when the essential spectrum of the linearization in the direction of the front touches the imaginary axis. At the linear level, the spectrum is stabilized by using an exponential weight. A priori estimates for the nonlinear terms of the equation governing the evolution of the perturbations of the front are obtained when perturbations belong to the intersection of the exponentially weighted space with the original space without a weight. 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