Abstract
Using the Fourier method, we obtain necessary and sufficient conditions for the existence of a classical solution of the mixed problem for a homogeneous wave equation with summable potential and fixed endpoints and also obtain an explicit representation of the solution in the form of a rapidly converging series.
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Translated from Itogi Nauki i Tekhniki, Seriya Sovremennaya Matematika i Ee Prilozheniya. Tematicheskie Obzory, Vol. 172, Proceedings of the Voronezh Winter Mathematical School “Modern Methods of Function Theory and Related Problems,” Voronezh, January 28 – February 2, 2019. Part 3, 2019.
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Kornev, V.V., Khromov, A.P. Classical Solution of the Mixed Problem for a Homogeneous Wave Equation with Fixed Endpoints. J Math Sci 267, 787–802 (2022). https://doi.org/10.1007/s10958-022-06170-7
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DOI: https://doi.org/10.1007/s10958-022-06170-7