For citation:
Khromov A. P. On Classic Solution of the Problem for a Homogeneous Wave Equation with Fixed End-Points and Zero Initial Velocity. Izvestiya of Saratov University. Mathematics. Mechanics. Informatics, 2019, vol. 19, iss. 3, pp. 280-288. DOI: 10.18500/1816-9791-2019-19-3-280-288, EDN: OWGYTU
On Classic Solution of the Problem for a Homogeneous Wave Equation with Fixed End-Points and Zero Initial Velocity
The paper gives necessary and sufficient conditions of classic solution for a homogeneous wave equation with a summable potential, fixed end-point, and zero initial velocity. With the use of Fourier method and Krylov method of improving series rate convergence an analogue of d’Alembert formula is derived in the form of exponentially convergent series. The paper essentially supports and extends the results of our work carried out in 2016. The suggested new method, based on the use of divergent (in Euler’s sense) series, is very economical in using well-known mathematical facts. It opens a perspective of considerable advancement in studying other boundary problems for partial differential equations.
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