A.P. Khromov, V.V. Kornev. Divergent series in the Fourier method for the wave equation ... P. 215-238

Series of formal solutions of two mixed problems for the wave equation are studied by a method based on the application of divergent series in the sense of Euler. The validity of this method is proved. The method is very economical in the use of well-known mathematical facts, which opens up the prospect of significant progress in the study of boundary value problems for partial differential equations.

Keywords: Fourier method, mixed problem, wave equation, divergent series, resolvent

Received March 18, 2021

Revised May 13, 2021

Accepted May 17, 2021

Avgust Petrovich Khromov, Dr. Phys.-Math. Sci., Prof., Saratov State University, Saratov, 410012 Russia, e-mail: KhromovAP@sgu.ru

Vladimir Victorovich Kornev, Cand. Sci. (Phys.-Math.), Saratov State University, Saratov, 410012 Russia, e-mail: KornevVV@sgu.ru

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Cite this article as: A.P. Khromov, V.V. Kornev. Divergent series in the Fourier method for the wave equation, Trudy Instituta Matematiki i Mekhaniki UrO RAN, 2021, vol. 27, no. 4, pp. 215–238.