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Existence of a smooth solution of one boundary-value problem

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Ukrainian Mathematical Journal Aims and scope

Abstract

We study a periodic boundary-value problem for the quasilinear equationu tt−uxx=F[u, ut], u(0, t)=u(π, t)=0,u(x, t+2π)=u(x, t). We establish conditions that guarantee the validity of the uniqueness theorem.

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References

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

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  2. L. A. Lyusternik and V. I. Sobolev,Elements of Functional Analysis [in Russian], Moscow, Nauka (1965).

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Authors and Affiliations

  1. Ternopol Pedagogical Institute, Ternopol

    N. G. Khoma

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  1. N. G. Khoma
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Translated from Ukrainskii Matematicheskii Zhurnal, Vol. 47, No. 12, pp. 1717–1719, December, 1995.

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Khoma, N.G. Existence of a smooth solution of one boundary-value problem. Ukr Math J 47, 1964–1967 (1995). https://doi.org/10.1007/BF01060973

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  • DOI: https://doi.org/10.1007/BF01060973

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