2017
DOI: 10.3934/dcdsb.2017168
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Stable foliations near a traveling front for reaction diffusion systems

Abstract: We establish the existence of a stable foliation in the vicinity of a traveling front solution for systems of reaction diffusion equations in one space dimension that arise in the study of chemical reactions models and solid fuel combustion. In this way we complement the orbital stability results from earlier papers by A. Ghazaryan, S. Schecter and Y. Latushkin. The essential spectrum of the differential operator obtained by linearization at the front touches the imaginary axis. In spaces with exponential weig… Show more

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“…An application of this approach to reaction diffusion equations can be found in a series of papers [9][10][11][12][13] which demonstrate the orbital stability of the traveling front by studying perturbations that are small in both unweighted and weighted Sobolev spaces. Subsequently, in [14], the authors established the existence of a stable foliation near the traveling front solution of the reaction diffusion system in one-dimensional space, i.e., the existence of a central manifold at each point on the front solution that attracts nearby solutions that are slightly perturbed to the front solution itself or to one of its translations. This result complements the orbit stability results in [11].…”
Section: Introductionmentioning
confidence: 99%
“…An application of this approach to reaction diffusion equations can be found in a series of papers [9][10][11][12][13] which demonstrate the orbital stability of the traveling front by studying perturbations that are small in both unweighted and weighted Sobolev spaces. Subsequently, in [14], the authors established the existence of a stable foliation near the traveling front solution of the reaction diffusion system in one-dimensional space, i.e., the existence of a central manifold at each point on the front solution that attracts nearby solutions that are slightly perturbed to the front solution itself or to one of its translations. This result complements the orbit stability results in [11].…”
Section: Introductionmentioning
confidence: 99%