Existence of global classical solutions of the initial-boundary value problem for some nonlinear wave equations (Q916900)

The author considers a hyperbolic initial-boundary problem in several space dimensions, admitting the presence of nonlinear terms in u and \(u_ z\) (but not in \(u_ x)\). Global existence of a classical solution is proved for initial data which are unbounded in \(H^ 3\times H^ 2\), provided the nonlinearities satisfy suitable strict monotonicity conditions.