Abstract: | We establish conditions for the existence of a smooth solution of a quasilinear hyperbolic equationu
tt
- uxx = ƒ(x, t, u, u, u
x),u (0,t) = u (π,t) = 0,u (x, t+ T) = u (x, t), (x, t) ∈ 0, π] ×R, and prove a theorem on the existence and uniqueness of a solution.
Translated from Ukrainskii Matematicheskii Zhurnal, Vol. 51, No. 11, pp. 1574–1576, November, 1999. |