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Global stability of traveling curved fronts in the Allen-Cahn equations

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  • This paper is concerned with the global stability of a traveling curved front in the Allen-Cahn equation. The existence of such a front is recently proved by constructing supersolutions and subsolutions. In this paper, we introduce a method to construct new subsolutions and prove the asymptotic stability of traveling curved fronts globally in space.
    Mathematics Subject Classification: 35K57, 35B35.


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