Abstract
<abstract><p>In this manuscript, we examine a nonlinear Cauchy problem aimed at describing the deformation of the deck of either a footbridge or a suspension bridge in a rectangular domain $ \Omega = (0, \pi)\times (-d, d) $, with $ d &lt; &lt; \pi $, incorporating hinged boundary conditions along its short edges, as well as free boundary conditions along its remaining free edges. We establish the existence of solutions and the exponential decay of energy.</p></abstract>
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