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Mixed problem for the string vibration equation with a time-dependent oblique derivative in the boundary condition

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Abstract

We obtain formulas for the classical solution of the mixed problem for the equation of vibrations of a half-bounded string for the case in which the boundary condition contains a directional (oblique) derivative with time-dependent direction. We find the limit values of the solution as the direction tends to a characteristic of the equation.

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References

  1. Lomovtsev, F.E., Necessary and Sufficient Conditions for the Unique Solvability of the Cauchy Problem for Second-Order Hyperbolic Differential Equations with Variable Domain of the Operator Coefficients, Differ. Uravn., 1992, vol. 28, no. 5, pp. 873–886.

    MATH  MathSciNet  Google Scholar 

  2. Lomovtsev, F.E., Second-Order Hyperbolic Operator-Differential Equations with Variable Domains of the Smooth Operator Coefficients, Dokl. Nats. Akad. Nauk Belarusi, 2001, vol. 45, no. 1, pp. 34–37.

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  3. Mikhlin, S.G., Kurs matematicheskoi fiziki (Course of Mathematical Physics), Moscow: Nauka, 1968.

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Authors and Affiliations

  1. Belarus State University, Minsk, Belarus

    S. N. Baranovskaya & N. I. Yurchuk

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  1. S. N. Baranovskaya
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  2. N. I. Yurchuk
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Original Russian Text © S.N. Baranovskaya, N.I. Yurchuk, 2009, published in Differentsial’nye Uravneniya, 2009, Vol. 45, No. 8, pp. 1188–1191.

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Baranovskaya, S.N., Yurchuk, N.I. Mixed problem for the string vibration equation with a time-dependent oblique derivative in the boundary condition. Diff Equat 45, 1212–1215 (2009). https://doi.org/10.1134/S0012266109080126

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  • DOI: https://doi.org/10.1134/S0012266109080126

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