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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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/

[1] Kornev V. V., Khromov A. P., “Skhodimost formalnogo resheniya po metodu Fure v smeshannoi zadache dlya prosteishego neodnorodnogo volnovogo uravneniya”, Mat. Mekh., 19 (2017), 41–44

[2] Natanson I. P., Teoriya funktsii veschestvennoi peemennoi, GITTL, M.-L., 1957 | MR

[3] Khardi G., Raskhodyaschiesya ryady, IL, M., 1951

[4] Khromov A. P., “Neobkhodimye i dostatochnye usloviya suschestvovaniya klassicheskogo resheniya smeshannoi zadachi dlya odnorodnogo volnovogo uravneniya v sluchae summiruemogo potentsiala”, Differ. uravn., 55:5 (2019), 717–731 | DOI | Zbl

[5] Khromov A. P., “Raskhodyaschiesya ryady i obobschennaya smeshannaya zadacha dlya volnovogo uravneniya”, Mat. 21 Mezhdunar. konf. «Sovremennye problemy teorii funktsii i ikh prilozheniya» (Saratov, 31 yanvarya — 4 fevralya 2022 g.), Saratov, 2022, 319–324

[6] Khromov A. P., Kornev V. V., “Raskhodyaschiesya ryady v metode Fure dlya volnovogo uravneniya”, Tr. in-ta mat. mekh. UrO RAN., 27:4 (2021), 215–238 | MR

[7] Eiler L., Differentsialnoe ischislenie, GITTL, M.-L., 1949