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Exponential Stability for the Generalized Korteweg-de Vries Equation in a Finite Interval with Weak Damping

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Abstract

The aim of this paper is to consider the generalized Korteweg-de Vries equation in a finite interval with a very weak localized dissipation. We obtain the globally uniformly exponentially stability of this equation. The main difficulty in this context comes from the structure of nonlinear term and the lack of regularity.

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Authors and Affiliations

  1. School of Mathematics and Statistics, Center for Mathematics and Interdisciplinary Sciences, Northeast Normal University, Changchun, 130024, P. R. China

    Mo Chen

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  1. Mo Chen
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Correspondence to Mo Chen.

Additional information

This work is supported by NSFC Grant (11701078), China Postdoctoral Science Foundation (2017M611292), the Fundamental Research Funds for the Central Universities(2412017QD002) and NSFC Grant (11601073).

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Chen, M. Exponential Stability for the Generalized Korteweg-de Vries Equation in a Finite Interval with Weak Damping. Indian J Pure Appl Math 49, 717–727 (2018). https://doi.org/10.1007/s13226-018-0297-0

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  • DOI: https://doi.org/10.1007/s13226-018-0297-0

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