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

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

doi:10.3934/dcdsb.2016.21.763

Article Contents

2016, Volume 21, Issue 3: 763-779. Doi: 10.3934/dcdsb.2016.21.763

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

1.
Department of Mathematics, National Central University, Chung-Li 32001
2.
Department of Applied Mathematics, National University of Kaohsiung, Kaohsiung 81148
3.
Department of Mathematics, Oklahoma State University, Stillwater, OK 74078
4.
Department of Financial and Computational Mathematics, Providence University, Taichung 43301

Received: March 31, 2014

Revised: August 31, 2015

Published: April 2016

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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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Mathematics Subject Classification: Primary: 35B45, 35B65; Secondary: 76B15, 76S05.

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References

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