Second order evolution equations with dynamic boundary conditions
The authors establish an existence and uniqueness result for the second-order abstract Cauchy problem \((Bu)''+ (Mu)'+ Nu= f\), \(Bu(0)= Bu_0\), \((Bu)'(0)= Bu_1\), where the nonlinear operators \(M\) and \(N\) and the linear operator \(B\) are suitably restricted and map a Hilbert space into its dual. The result is shown to be directly applicable to weak formulations of certain initial-boundary value problems modelling the dynamic vibrations of rods and beams with attached tip masses at their free ends.
scientific article; zbMATH DE number 902473
scientific article