Coupled string-beam equations as a model of suspension bridges.
The authors extend results of a recent paper by \textit{G. Tajčová} [Appl. Math., Praha 42, No. 6, 451--480 (1997; Zbl 1042.74535)] to a broader class of input parameters. A system of two nonlinear partial differential equations represents a model of forced vibration of a central span of a suspension bridge, i.e.\ of the roadbed connected with the main cable by a system of vertical stays. Using a fairly sophisticated functional analytical method, the authors prove (i) the existence of a solution for any square-integrable loading and (ii) the uniqueness of the solution and some regularity, provided the external forcing terms are small in a certain sense and the weight of the cable is sufficiently small in comparison with the weight of the roadbed.
scientific article; zbMATH DE number 2165519