Geodesic
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, Tome 19 (2019) no. 3, pp. 280-288

Voir la notice de l'article provenant de la source Math-Net.Ru

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. 
@article{ISU_2019_19_3_a2,
     author = {A. P. Khromov},
     title = {On classic solution of the problem for a homogeneous wave equation with fixed end-points and zero initial velocity},
     journal = {Izvestiya of Saratov University. Mathematics. Mechanics. Informatics},
     pages = {280--288},
     publisher = {mathdoc},
     volume = {19},
     number = {3},
     year = {2019},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/ISU_2019_19_3_a2/}
}
TY  - JOUR
AU  - A. P. Khromov
TI  - On classic solution of the problem for a homogeneous wave equation with fixed end-points and zero initial velocity
JO  - Izvestiya of Saratov University. Mathematics. Mechanics. Informatics
PY  - 2019
SP  - 280
EP  - 288
VL  - 19
IS  - 3
PB  - mathdoc
UR  - http://geodesic.mathdoc.fr/item/ISU_2019_19_3_a2/
LA  - ru
ID  - ISU_2019_19_3_a2
ER  - 
%0 Journal Article
%A A. P. Khromov
%T On classic solution of the problem for a homogeneous wave equation with fixed end-points and zero initial velocity
%J Izvestiya of Saratov University. Mathematics. Mechanics. Informatics
%D 2019
%P 280-288
%V 19
%N 3
%I mathdoc
%U http://geodesic.mathdoc.fr/item/ISU_2019_19_3_a2/
%G ru
%F ISU_2019_19_3_a2
A. P. Khromov. 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, Tome 19 (2019) no. 3, pp. 280-288. http://geodesic.mathdoc.fr/item/ISU_2019_19_3_a2/