“…In addition, G.G. Doronin et al [6] studied the following nonlinear hyperbolic problem with nonlinear second-order boundary conditions: u tt − a(u)u xx + g(u t ) = f (x, t), (x, t) ∈ (0, 1) × (0, T ), (1.4) u(0, t) = 0, u x + K(u)u tt + h(u t ) (1, t) = 0, (1.5) u(x, 0) = u 0 (x), u t (x, 0) = u 1 (x), x ∈ (0, 1). (1.6) It was proved that the problem (1.4)-(1.6) has global strong solution without any restrictions on the size of initial data and f by the method of Galerkin and compactness arguments.…”