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Well-Posedness Results and Dissipative Limit of High Dimensional KdV-Type Equations

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Abstract

Considered in this work is an n-dimensional dissipative version of the Korteweg–de Vries (KdV) equation. Our goal here is to investigate the well-posedness issue for the associated initial value problem in the anisotropic Sobolev spaces. We also study well-posedness behavior of this equation when the dissipative effects are reduced.

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Authors and Affiliations

  1. Instituto de Matemática, UFRJ, Av. Horácio Macedo, Centro de Tecnologia Cidade Universitária, Ilha do Fundão, Rio de Janeiro, RJ, 21941-972, Brazil

    Xavier Carvajal

  2. School of Mathematics and Computer Science, Damghan University, 36715-364, Damghan, Iran

    Amin Esfahani

  3. IMECC-UNICAMP, Rua Sérgio Buarque de Holanda, 651, Cidade Universitária, Campinas, SP, 13083-859, Brazil

    Mahendra Panthee

Authors
  1. Xavier Carvajal
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  2. Amin Esfahani
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  3. Mahendra Panthee
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Corresponding author

Correspondence to Mahendra Panthee.

Additional information

XC acknowledges the support from CNPq-Brazil 304036/2014-5. MP was partially supported from FAPESP-Brazil 2012/20966-4, 2016/25864-6 and CNPq-Brazil 479558/2013-2, 305483/2014-5.

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Carvajal, X., Esfahani, A. & Panthee, M. Well-Posedness Results and Dissipative Limit of High Dimensional KdV-Type Equations. Bull Braz Math Soc, New Series 48, 505–550 (2017). https://doi.org/10.1007/s00574-017-0034-z

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  • DOI: https://doi.org/10.1007/s00574-017-0034-z

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