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Abstract
The extensible beam equation proposed by Woinowsky-Krieger is a fourth order dispersive equation with nonlocal nonlinear terms. In this paper we study the Cauchy problem of the extended model by Ball who proposed the following model with external and structural damping terms:
For this represents a Kelvin–Voigt damping. We show the unique global existence of solutions for this problem and give a precise description of the decay of solutions in time.
Acknowledgements
The article was written when the second author visited the University of Konstanz between April 2014 and February 2015. He expresses his sincere gratitude to the kind hospitality of the people at the University of Konstanz.
Notes
No potential conflict of interest was reported by the authors.
Additional information
Funding
The second author is partially supported by the Japan Ministry of Education, Science, Sports and Culture, Grant-in-Aid for Scientific Research (C) [No. 25400172].