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.
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References
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Translated from Ukrainskii Matematicheskii Zhurnal, Vol. 51, No. 11, pp. 1574–1576, November, 1999.
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Dombrovskii, I.V. On a smooth solution of a nonlinear periodic boundary-value problem. Ukr Math J 51, 1779–1781 (1999). https://doi.org/10.1007/BF02525264
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DOI: https://doi.org/10.1007/BF02525264