Global existence and asymptotic behaviour for systems of nonlinear hyperbolic equations

Abstract

We consider the initial-boundary value problem for a class of nonlinear hyperbolic equations system in a bounded domain. Using the potential well theory, the existence of global solutions is investigated. We also established the asymptotic behaviour of global solutions as t → + ∞ by applying the multiplier method.

Keywords:

• systems of nonlinear hyperbolic equations
• initial-boundary value problem
• global solutions
• asymptotic behaviour

AMS Subject Classifications::

• 35B40
• 35L75
• 35L05

Acknowledgements

This research was supported by the National Natural Science Foundation of China (No. 61273016), the Natural Science Foundation of Zhejiang Province (No. Y6100016), the Middle-aged and Young Leader in Zhejiang University of Science and Technology (2008–2012) and Interdisciplinary Pre-research Project of Zhejiang University of Science and Technology (2010–2012).