Stability results of a suspension-bridge with nonlinear damping modulated by a time dependent coefficient

 Al-Gharabli, Mohammad M. and Messaoudi, Salim A.

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The main goal of this work is to investigate the following weakly damped nonlinear suspension-bridge equation

    \[u_{tt}(x,y,t)+\Delta ^2 u(x,y,t) +\alpha(t) g(u_t)=0,\]

and establish explicit and general decay results for the energy of solutions of the problem. Our decay results depend on the functions \alpha and g and obtained without any restriction growth assumption on g at the origin. The multiplier method, the properties of the convex and the dual of the convex functions, Jensen’s inequality and the generalized Young inequality are used to establish the stability results.


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 Al-Gharabli, Mohammad M., Messaoudi, Salim A.