2019
Том 71
№ 9

All Issues

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

Dobrynskii V. A.

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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.

English version (Springer): Ukrainian Mathematical Journal 51 (1999), no. 11, pp 1779-1781.

Citation Example: Dobrynskii V. A. On a smooth solution of a nonlinear periodic boundary-value problem // Ukr. Mat. Zh. - 1999. - 51, № 11. - pp. 1574–1576.

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