In this paper we provide a local well posedness result for a quasilinear beam-wave system of equations on a one-dimensional spatial domain under periodic and Dirichlet boundary conditions. This kind of systems provides a refined model for the time-evolution of suspension bridges, where the beam and wave equations describe respectively the longitudinal and torsional motion of the deck. The quasilinearity arises when one takes into account the nonlinear restoring action of deformable cables and hangers. To obtain the a priori estimates for the solutions of the linearized equation we build a modified energy by means of paradifferential changes of variables. Then we construct the solutions of the nonlinear problem by using a quasilinear iterative scheme à la Kato.
Feola, R., Giuliani, F., Iandoli, F., Massetti, J.E. (In corso di stampa). Local well posedness for a system of quasilinear PDEs modelling suspension bridges. NONLINEAR ANALYSIS, 240 [10.1016/j.na.2023.113442].
Local well posedness for a system of quasilinear PDEs modelling suspension bridges
Roberto Feola;Jessica Elisa Massetti
In corso di stampa
Abstract
In this paper we provide a local well posedness result for a quasilinear beam-wave system of equations on a one-dimensional spatial domain under periodic and Dirichlet boundary conditions. This kind of systems provides a refined model for the time-evolution of suspension bridges, where the beam and wave equations describe respectively the longitudinal and torsional motion of the deck. The quasilinearity arises when one takes into account the nonlinear restoring action of deformable cables and hangers. To obtain the a priori estimates for the solutions of the linearized equation we build a modified energy by means of paradifferential changes of variables. Then we construct the solutions of the nonlinear problem by using a quasilinear iterative scheme à la Kato.I documenti in IRIS sono protetti da copyright e tutti i diritti sono riservati, salvo diversa indicazione.
