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JOURNALS // Zhurnal Vychislitel'noi Matematiki i Matematicheskoi Fiziki // Archive

Zh. Vychisl. Mat. Mat. Fiz., 2018 Volume 58, Number 9, Pages 1583–1596 (Mi zvmmf10775)

This article is cited in 2 papers

Mixed problem for a homogeneous wave equation with a nonzero initial velocity

A. P. Khromov

Saratov State University, Saratov, Russia

Abstract: A mixed problem for a homogeneous wave equation with fixed ends, a summable potential, and a nonzero initial velocity is studied. Using the resolvent approach and developing the Krylov method for accelerating the convergence of Fourier series, a classical solution is obtained by the Fourier method under minimal conditions on the smoothness of the initial data and a generalized solution in the case of the initial velocity represented by an arbitrary summable function is found.

Key words: Fourier method, formal solution, wave equation, resolvent.

UDC: 519.633

Received: 18.05.2017

DOI: 10.31857/S004446690002535-9


 English version:
Computational Mathematics and Mathematical Physics, 2018, 58:9, 1531–1543

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