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arXiv · 1505.00425

Well-posedness of the two-dimensional generalized Benjamin-Bona-Mahony equation on the upper half plane

Ying-Chieh Lin·C. H. Arthur Cheng·John M. Hong·Jiahong Wu·Juan-Ming Yuan
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Abstract

This paper focuses on the two-dimensional Benjamin-Bona-Mahony and Benjamin-Bona-Mahony-Burgers equations with a general flux function. The aim is at the global (in time) well-posedness of the initial-and boundary-value problem for these equations defined in the upper half-plane. Under suitable growth conditions on the flux function, we are able to establish the global well-posedness in a Sobolev class. When the initial- and boundary-data become more regular, the corresponding solutions are shown to be classical. In addition, the continuous dependence on the data is also obtained.

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Ying-Chieh Lin, C. H. Arthur Cheng, John M. Hong, Jiahong Wu, Juan-Ming Yuan. 2015-05-03. Well-posedness of the two-dimensional generalized Benjamin-Bona-Mahony equation on the upper half plane. https://arxiv.org/abs/1505.00425

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