Global solvability for the quasilinear damped wave equation with nonlinear second-order boundary conditions (Q1612626)

The authors prove global existence, uniqueness and stability of a strong solution to the quasilinear equation \(u_{tt}-a(t)u_{xx}+g(u_{t})=f\) satisfying nonlinear boundary conditions \((u_{x}+K(u)u_{tt}+h(u_{t}))(1,t)=0, u(0,t)=0\) and arbitrary initial data, where the functions \(g,K,h\) satisfy growth conditions. The nonlinear terms and higher derivatives of the problem arise in physical applications.