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Abstract
The existence of global weak solutions for a dissipative model equation for shallow water wave of moderate amplitude is studied in the space without the sign condition on the initial value by employing the limit technique of viscous approximation. A new one-sided lower bound and the higher integrability estimate act a key role in our analysis. Our results partly extend the work of Coclite et al. on the existence of global weak solutions to the generalized hyperlastic-rod equation.
Acknowledgements
We would like to express our thanks to the anonymous referees for pointing out some mistakes and giving some valuable suggestions which greatly improved the original version of our paper.
Notes
No potential conflict of interest was reported by the authors.
Additional information
Funding
Guo’s work is supported by Sichuan Province University Key Laboratory of Bridge Non-destruction Detecting and Engineering Computing [grant number 2013QZJ02], [grant number 2014QYJ03]; SUSER [grant number 2014RC03] and Australian Research Council Funded Project (Project ID FT140101112). Lai’s work is supported by Natural Science Foundation of China NSFC [grant number 11471263].