Abstract
We study a boundary-value periodic problem for the quasilinear equationu ff −u xx =F[u,u f u x ],u(0,t) =u (π,t),u (x, t + π/q) =u(x, t), 0 ≤x ≤π,t ∈ ℝ,q ∈ ℕ. We establish conditions under which the theorem on the uniqueness of a smooth solution is true.
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References
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.
O. Vejvoda and M. Shtedry, “Existence of classical periodic solutions of the wave equation: Relationship between the number-theoretic character of the period and geometric properties of solutions,”Differents. Uravn.,20, No. 10, 1733–1739 (1984).
Yu. A. Mitropol’skii and N. G. Khoma, “Periodic solutions of second-order quasilinear hyperbolic equations,”Ukr. Mat. Zh.,47, No. 10, 1370–1375 (1995).
N. G. Khoma, “Existence of a smooth solution of one boundary-value problem,”Ukr. Mat. Zh.,47, No. 12, 1717–1719 (1995).
L. A. Lyusternik and V. I. Sobolev,Elements of Functional Analysis [in Russian], Moscow, Nauka 1965.
Ph. Hartman,Ordinary Differential Equations [Russian translation], Mir, Moscow 1970.
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Khoma, L.G., Khoma, N.G. Generalized periodic solutions of quasilinear equations. Ukr Math J 48, 453–459 (1996). https://doi.org/10.1007/BF02378534
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DOI: https://doi.org/10.1007/BF02378534