We study the fourth order semilinear suspension bridge problem with restoring force h(u) and linear damping \(\delta u_{t}\). Using the multiplier method, we first establish the observability inequality of the corresponding system without damping term. Then we show an equivalence between observability and exponential stabilization of this system by using an appropriate decomposition technique and the semigroup method.

中文翻译：

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悬索桥问题的内部可观性与指数稳定之间的等价关系

我们研究了具有恢复力h（u）和线性阻尼\（\ delta u_ {t} \）的四阶半线性悬索桥问题。使用乘数法，我们首先建立了没有阻尼项的相应系统的可观测性不等式。然后，使用适当的分解技术和半群方法，证明了该系统的可观测性与指数稳定之间的等价性。