Abstract
In this article, we study the weak dissipative Kirchhoff equation \({u_{tt}} - M\left( {\left\| {\nabla u} \right\|_2^2} \right)\Delta u + b\left( x \right){u_t} + f\left( u \right) = 0\), under nonlinear damping on the boundary \(\frac{{\partial u}}{{\partial v}} + \alpha \left( t \right)g\left( {{u_t}} \right) = 0\). We prove a general energy decay property for solutions in terms of coefficient of the frictional boundary damping. Our result extends and improves some results in the literature such as the work by Zhang and Miao (2010) in which only exponential energy decay is considered and the work by Zhang and Huang (2014) where the energy decay has been not considered.
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The author would like to thank the referees for useful comments and suggestions on the first version of the manuscript.
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Peyravi, A. General energy decay of solutions for a weakly dissipative Kirchhoff equation with nonlinear boundary damping. Acta Math. Appl. Sin. Engl. Ser. 33, 401–408 (2017). https://doi.org/10.1007/s10255-017-0669-y
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DOI: https://doi.org/10.1007/s10255-017-0669-y