Abstract
In three spaces, we find exact classical solutions of the boundary-value periodic problem utt - a2uxx = g(x, t) u(0, t) = u(π, t) = 0, u(x, t + T) = u(x, t), x ∈ ℝ, t ∈ ℝ. We study the periodic boundary-value problem for a quasilinear equation whose left-hand side is the d’Alembert operator and whose right-hand side is a nonlinear operator.
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Translated from Ukrainskii Matematicheskii Zhurnal, Vol. 50, No. 12, pp. 1680–1685, December, 1998.
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Khoma, N.G. Linear periodic boundary-value problem for a second-order hyperbolic equation. II. Quasilinear problem. Ukr Math J 50, 1917–1923 (1998). https://doi.org/10.1007/BF02514207
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DOI: https://doi.org/10.1007/BF02514207