Abstract
We find conditions for the existence of the classical solution of the boundary-value problem u tt -u xx = f(x,t), u(0,t)=u(π, t)=0, u(x, 0)=u(x, 2π).
References
Yu. A. MitropoFskii, G. P. Khoma, and M. I. Gromyak, Asymptotic Methods for the Investigation of Quasiwave Hyperbolic Equations [in Russian] Naukova Dumka, Kiev 1991.
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Khoma, S.G. Solution of one boundary-value problem for a hyperbolic equation of the second order. Ukr Math J 52, 655–657 (2000). https://doi.org/10.1007/BF02515407
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DOI: https://doi.org/10.1007/BF02515407