# American Institute of Mathematical Sciences

January  2018, 38(1): 397-429. doi: 10.3934/dcds.2018019

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

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

Received  September 2016 Revised  August 2017 Published  September 2017

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.

Citation: Hongqiu Chen. Well-posedness for a higher-order, nonlinear, dispersive equation on a quarter plane. Discrete & Continuous Dynamical Systems - A, 2018, 38 (1) : 397-429. doi: 10.3934/dcds.2018019
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