Linear periodic boundary-value problem for a second-order hyperbolic equation. II. Quasilinear problem - Khoma, N. H. (Ukrains’kyi Matematychnyi Zhurnal, 1998)
In three spaces, we find exact classical solutions of the boundary-value periodic problem utt - a2uxx = g(x, t) u(0, t) = u(π, t) = 0, u(x, t + T) = u(x, t), x ∈ ℝ, t ∈ ℝ. We study the periodic boundary-value problem for a quasilinear equation whose left-hand side is the d’Alembert operator and whose right-hand side is a nonlinear operator.