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Open Access Research

General decay for a wave equation of Kirchhoff type with a boundary control of memory type

Shun-Tang Wu

Author Affiliations

General Education Center, National Taipei University of Technology, Taipei 106, Taiwan

Boundary Value Problems 2011, 2011:55  doi:10.1186/1687-2770-2011-55

Published: 23 December 2011

Abstract

A nonlinear wave equation of Kirchhoff type with memory condition at the boundary in a bounded domain is considered. We establish a general decay result which includes the usual exponential and polynomial decay rates. Furthermore, our results allow certain relaxation functions which are not necessarily of exponential and polynomial decay. This improves earlier results in the literature.

MSC: 35L05; 35L70; 35L75; 74D10.

Keywords:
general decay; wave equation; relaxation; memory type; Kirchhoff type; nondissipative