Geodesic
Generalized mixed problem for the simplest wave equation and its applications
Itogi nauki i tehniki. Sovremennaâ matematika i eë priloženiâ. Tematičeskie obzory, Proceedings of the Voronezh international winter mathematical school "Modern methods of function theory and related problems", Voronezh, January 27 - February 1, 2023, Part 3, Tome 229 (2023), pp. 83-89

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In this paper, we present results for generalized homogeneous and inhomogeneous mixed problems for the wave equation based on the operation of integrating a divergent series of a formal solution using the method of separation of variables. A solution to the generalized mixed problem for an inhomogeneous equation is found under the assumption that the function characterizing the inhomogeneity is locally summable. As an application, a mixed problem with nonzero potential is considered.
Mots-clés : divergent series
Keywords: wave equation, mixed problem 
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     title = {Generalized mixed problem for the simplest wave equation and its applications},
     journal = {Itogi nauki i tehniki. Sovremenna\^a matematika i e\"e prilo\v{z}eni\^a. Temati\v{c}eskie obzory},
     pages = {83--89},
     publisher = {mathdoc},
     volume = {229},
     year = {2023},
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     url = {http://geodesic.mathdoc.fr/item/INTO_2023_229_a7/}
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A. P. Khromov. Generalized mixed problem for the simplest wave equation and its applications. Itogi nauki i tehniki. Sovremennaâ matematika i eë priloženiâ. Tematičeskie obzory, Proceedings of the Voronezh international winter mathematical school "Modern methods of function theory and related problems", Voronezh, January 27 - February 1, 2023, Part 3, Tome 229 (2023), pp. 83-89. http://geodesic.mathdoc.fr/item/INTO_2023_229_a7/