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JOURNALS // Doklady Rossijskoj Akademii Nauk. Mathematika, Informatika, Processy Upravlenia // Archive

Dokl. RAN. Math. Inf. Proc. Upr., 2024 Volume 516, Pages 26–30 (Mi danma509)

MATHEMATICS

Generalized solution of a mixed problem for the wave equation with a nonsmooth right-hand side

I. S. Lomov

Lomonosov Moscow State University, Moscow, Russia

Abstract: A generalized solution of a mixed problem for the wave equation is constructed under minimal conditions on the right side of the equation. The solution is represented as a series from the Fourier method, and its sum is found. The form of a generalized solution of a mixed problem for an inhomogeneous telegraph equation is given.

Keywords: wave equation, telegraph equation, Fourier method, Cauchy–Poincaré method.

UDC: 517.956.32+517.984

Presented: I. A. Sokolov
Received: 02.10.2023
Revised: 09.02.2024
Accepted: 09.02.2024

DOI: 10.31857/S2686954324020052


 English version:
Doklady Mathematics, 2024, 109:2, 121–124

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© Steklov Math. Inst. of RAS, 2025