Modelling And Boundary Control Of Conductor Galloping

On a Rayleigh Wave Equation with Boundary Damping

“…It will be shown that the initial-boundary value problem (19) - (23) is well-posed for all times t > 0. To show the well-posedness of the problem a semigroup approach will be used.…”

“…Simple models which describe these oscillations can be expressed in initial-boundary value problems for wave equations like in [1,2,3,4,5,6,11,19] or for beam equations like in [7,8,9,10,18]. Simple models which describe these oscillations can involve linear or nonlinear second and fourth order partial differential equations with classical or non-classical boundary conditions.…”

“…These vibrations can give rise to for instance material fatigue. To suppress these oscillations various types of dampers have been applied in practice (see [18,19]). …”

“…More complicated, non-classical boundary conditions ( see for instance [2,3,10,11,12,13,14]) have been considered only for linear partial differential equations. For nonlinear wave equations with boundary damping the approximations have been obtained only numerically(see for instance [19]). In [19] it has been shown that for large values of the damping parameter the solutions tend to zero.…”

“…For nonlinear wave equations with boundary damping the approximations have been obtained only numerically(see for instance [19]). In [19] it has been shown that for large values of the damping parameter the solutions tend to zero. It is, however, not clear how and for what values of the damping parameter the solutions will tend to zero (or not).…”