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The Korteweg–de Vries equation on a metric star graph

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Abstract

We prove local well-posedness for the Cauchy problem associated with Korteweg–de Vries equation on a metric star graph with three semi-infinite edges given by one negative half-line and two positive half-lines attached to a common vertex, for two classes of boundary conditions. The results are obtained in the low regularity setting by using the Duhamel boundary forcing operator, in context of half-lines, introduced by Colliander and Kenig (Commun Partial Differ Equ 27(11/12): 2187–2266, 2002), and extended by Holmer (Commun Partial Differ Equ 31:1151–1190, 2006) and Cavalcante (Differ Integral Equ 30(7/8):521–554, 2017).

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Acknowledgements

The author wishes to thank the Centro de Modelamiento Matemático (CMM) and Universidad de Chile and Núcleo Milenio CAPDE, for the financial support and nice scientific infrastructure that allowed to conclude the paper during his postdoctoral stay.

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  1. Instituto de Matemática, Universidade Federal de Alagoas, Maceió, Brazil

    Márcio Cavalcante

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  1. Márcio Cavalcante
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Cavalcante, M. The Korteweg–de Vries equation on a metric star graph. Z. Angew. Math. Phys. 69, 124 (2018). https://doi.org/10.1007/s00033-018-1018-6

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  • DOI: https://doi.org/10.1007/s00033-018-1018-6

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