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Initial-boundary value problem with a nonlocal boundary condition for a multidimensional hyperbolic equation

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Abstract

We consider a mixed initial-boundary value problem for a multidimensional (with respect to the space variables) hyperbolic equation with a nonlocal boundary condition containing an integral of the desired solution. We prove the unique solvability of the problem in the space W 12 .

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References

  1. Pul’kina, L.S., in Neklassicheskie uravneniya matematicheskoi fiziki (Nonclassical Equations of Mathematical Physics), Novosibirsk, 2005, pp. 231–239.

  2. Dmitriev, V.B., Vestn. Samarsk. Gos. Univ., 2006, no. 2 (42), pp. 15–27.

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Original Russian Text © L.S. Pul’kina, 2008, published in Differentsial’nye Uravneniya, 2008, Vol. 44, No. 8, pp. 1084–1089.

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Pul’kina, L.S. Initial-boundary value problem with a nonlocal boundary condition for a multidimensional hyperbolic equation. Diff Equat 44, 1119–1125 (2008). https://doi.org/10.1134/S0012266108080090

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  • DOI: https://doi.org/10.1134/S0012266108080090

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