2019
Том 71
№ 8

All Issues

Dobrynskii V. A.

Articles: 1
Brief Communications (Ukrainian)

On a smooth solution of a nonlinear periodic boundary-value problem

Dobrynskii V. A.

↓ Abstract   |   Full text (.pdf)

Ukr. Mat. Zh. - 1999. - 51, № 11. - pp. 1574–1576

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.