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Global Carleman estimate for the Kawahara equation and its applications

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    * Corresponding author
This work is supported by NSFC Grant (11601073), NSFC Grant (11701078), China Postdoctoral Science Foundation (2017M611292), the Fundamental Research Funds for the Central Universities (2412017QD002), and NSFC Grant (11626043).
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  • In this paper, we establish a global Carleman estimate for the Kawahara equation. Based on this estimate, we obtain the Unique Continuation Property (UCP) for this equation and the global exponential stability for the Kawahara equation with a very weak localized dissipation.

    Mathematics Subject Classification: Primary: 35Q53; Secondary: 93D15, 35Q35.


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