Well-posedness for a higher-order, nonlinear, dispersive equation on a quarter plane

Hongqiu Chen

doi:10.3934/dcds.2018019

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2018, Volume 38, Issue 1: 397-429. Doi: 10.3934/dcds.2018019

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Well-posedness for a higher-order, nonlinear, dispersive equation on a quarter plane

Hongqiu Chen

Department of Mathematical Sciences, The University of Memphis, Memphis, TN 38152, USA

Received: August 31, 2016

Revised: July 31, 2017

Published: October 2017

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Abstract

The focus of the current paper is the higher order nonlinear dispersive equation which models unidirectional propagation of small amplitude long waves in dispersive media. The specific interest is in the initial-boundary value problem where spatial variable lies in $\mathbb R^+,$ namely, quarter plane problem. With proper requirement on initial and boundary condition, we show local and global well posedness.

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Mathematics Subject Classification: Primary:35Q35, 35Q53, 76B03, 76B15.

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References

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