Geodesic
Classical solution of the mixed problem for a homogeneous wave equation with fixed endpoints
Itogi nauki i tehniki. Sovremennaâ matematika i eë priloženiâ. Tematičeskie obzory, Proceedings of the Voronezh Winter Mathematical School "Modern Methods of Function Theory and Related Problems." January 28 – February 2, 2019. Part 3, Tome 172 (2019), pp. 119-133

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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.
Keywords: mixed task, wave equation, summable potential, Fourier method. 
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     title = {Classical solution of the mixed problem for a homogeneous wave equation with fixed endpoints},
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V. V. Kornev; A. P. Khromov. Classical solution of the mixed problem for a homogeneous wave equation with fixed endpoints. Itogi nauki i tehniki. Sovremennaâ matematika i eë priloženiâ. Tematičeskie obzory, Proceedings of the Voronezh Winter Mathematical School "Modern Methods of Function Theory and Related Problems." January 28 – February 2, 2019. Part 3, Tome 172 (2019), pp. 119-133. http://geodesic.mathdoc.fr/item/INTO_2019_172_a9/