Geodesic
On a Cauchy problem with periodic initial values
Čebyševskij sbornik, Tome 22 (2021) no. 5, pp. 16-24

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In the paper, the method of exponential sums is applied to the solution of partial differential equation. At the initial step, the authors decrease the dimension of the problem by separation of variables. Thus the initial problem reduses to the system of the ordinary differential equations. This allows one to use Fourier analysis.
Keywords: the wave equation, Helmgoltz equation, the separation of varuales method, the Fourier analysis. 
L. G. Arkhipova; V. N. Chubarikov. On a Cauchy problem with periodic initial values. Čebyševskij sbornik, Tome 22 (2021) no. 5, pp. 16-24. http://geodesic.mathdoc.fr/item/CHEB_2021_22_5_a2/
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