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Mathematical modelling of cable stayed bridges: existence, uniqueness, continuous dependence on data, homogenization of cable systems. (English) Zbl 1099.35151

Summary: A model of a cable stayed bridge is proposed. This model describes the behaviour of the center span, the part between pylons, hung on one row of cable stays. The existence, the uniqueness of a solution of a time independent problem and the continuous dependence on data are proved. The existence and the uniqueness of a solution of a linearized dynamic problem are proved. A homogenizing procedure making it possible to replace cables by a continuous system is proposed. A nonlinear dynamic problem connected with the homogenizing procedure is proposed and the existence and uniqueness of a solution are proved.

MSC:

35Q72 Other PDE from mechanics (MSC2000)
35B05 Oscillation, zeros of solutions, mean value theorems, etc. in context of PDEs
35B35 Stability in context of PDEs
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