On a smooth solution of a boundary-value problem - Tsynalko, P. V. (Ukrains’kyi Matematychnyi Zhurnal, 1998)
We study a periodic boundary-value problem for the quasilinear equation u tt −u xx =F[u, u t , u x ], u(x, 0)=u(x, π)=0, u(x + ω, t) = u(x, t), x ∈ ℝ t ∈ [0, π], and establish conditions that guarantee the validity of a theorem on unique solvability.