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Modified Zakharov-Kuznetsov Equation Posed on a Half-Strip

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Abstract

An initial-boundary value problem for the modified 2D Zakharov–Kuznetsov equation posed on a right-hand half-strip is considered. Studied here is the critical power in nonlinearity which is a novelty for unbounded domains even with the homogeneous boundary condition. The results on existence, uniqueness and asymptotic behavior of solutions are presented. Partially, exponential-in-time decay of strong solutions in appropriated norms is proved.

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Notes

  1. See the Remark below

  2. We will use this kind of proceeding to get the resulting identity in forthcoming estimates

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Acknowledgements

We thank very much Jerry Bona and Nikolai Larkin for their fruitful and motivating discussions. We appreciate also all the Referee’s comments which help essentially to improve the text.

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  1. Departamento de Matemática, Universidade Estadual de Maringá, Av. Colombo 5790: Agência UEM, Maringá, PR, 87020-900, Brazil

    M. Castelli, G. Doronin & M. V. Padilha

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  1. M. Castelli
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  2. G. Doronin
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  3. M. V. Padilha
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Correspondence to G. Doronin.

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Castelli, M., Doronin, G. & Padilha, M.V. Modified Zakharov-Kuznetsov Equation Posed on a Half-Strip. Appl Math Optim 85, 34 (2022). https://doi.org/10.1007/s00245-022-09877-w

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