Blow up oscillating solutions to some nonlinear fourth order differential equations
The authors consider the following non-linear differential equation: \[ w^{(4)}(s) + k{w}''(s) + f(w(s)) = 0, \] where \(s,k \in \mathbb R\), \(f\) is a locally Lipschitz function. They give theoretical and numerical evidence of solutions blowing up in finite time with infinitely many wild oscillations. An explicit example is presented where this phenomenon occurs. The authors also discuss possible applications to biharmonic partial differential equations and to the suspension bridge model, and give a possible new explanation of the collapse of bridges.
scientific article; zbMATH DE number 5959720
scientific article