A nonlinear beam equation
The aim of this paper is to prove the existence and uniqueness of weak solutions to a nonlinear beam equation with linear boundary and initial conditions. The nonlinear term appearing in the beam equation is \([g(w_{xx})]_{xx}\), where \(w=w(x,t)\) is the deflection, \(g\) is a given nonlinear function satisfying a local Lipschitz condition only. The presented method can be extended to a general second-order evolution system with hysteresis.
scientific article; zbMATH DE number 1878862