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On a smooth solution of a boundary-value problem

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Abstract

We study a periodic boundary-value problem for the quasilinear equation u tt −u xx =F[u, u t , u x ], u(x, 0)=u(x, π)=0, u(x + ω, t) = u(x, t), x ∈ ℝ t ∈ [0, π], and establish conditions that guarantee the validity of a theorem on unique solvability.

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References

  1. N. G. Khoma and P. V. Tsynaiko, “Smooth solution of one boundary-value problem,” Ukr. Mat. Zh., 49, No. 12, 1712–1716 (1997).

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  2. Yu. A. Mitropol’skii, G. P. Khoma, and M. I. Gromyak, Asymptotic Methods for Investigation of Quasiwave Equations of Hyperbolic Type [in Russian], Naukova Dumka, Kiev (1991).

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  3. F. Hartmann, Ordinary Differential Equations [Russian translation], Mir, Moscow (1970).

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Authors and Affiliations

  1. Ternopol Pedagogic Institute, Ternopol

    P. V. Tsynaiko

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  1. P. V. Tsynaiko
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Translated from Ukrainskii Matematicheskii Zhurnal, Vol. 50, No. 9, pp. 1293–1296, September, 1998.

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Tsynaiko, P.V. On a smooth solution of a boundary-value problem. Ukr Math J 50, 1478–1482 (1998). https://doi.org/10.1007/BF02525257

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  • DOI: https://doi.org/10.1007/BF02525257

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