Geodesic
Classical Solutions of a Multidimensional Hyperbolic Differential--Difference Equation with Shifts of Various Directions in the Potentials
Matematičeskie zametki, Tome 112 (2022) no. 6, pp. 810-819

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

We study the existence of smooth solutions of a multidimensional hyperbolic equation containing the sum of differential operators and shift operators along arbitrary spatial coordinate directions. For this equation, we construct a three-parameter family of solutions. It is proved that the resulting solutions are classical under the condition that the real part of the symbol of the differential–difference operator in the equation is positive. Classes of equations for which this condition holds are given.
Keywords: hyperbolic equation, differential–difference equation, classical solution, operational scheme
Mots-clés : Fourier transform. 
@article{MZM_2022_112_6_a1,
     author = {N. V. Zaitseva},
     title = {Classical {Solutions} of a {Multidimensional} {Hyperbolic} {Differential--Difference} {Equation} with {Shifts} of {Various} {Directions} in the {Potentials}},
     journal = {Matemati\v{c}eskie zametki},
     pages = {810--819},
     publisher = {mathdoc},
     volume = {112},
     number = {6},
     year = {2022},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/MZM_2022_112_6_a1/}
}
TY  - JOUR
AU  - N. V. Zaitseva
TI  - Classical Solutions of a Multidimensional Hyperbolic Differential--Difference Equation with Shifts of Various Directions in the Potentials
JO  - Matematičeskie zametki
PY  - 2022
SP  - 810
EP  - 819
VL  - 112
IS  - 6
PB  - mathdoc
UR  - http://geodesic.mathdoc.fr/item/MZM_2022_112_6_a1/
LA  - ru
ID  - MZM_2022_112_6_a1
ER  - 
%0 Journal Article
%A N. V. Zaitseva
%T Classical Solutions of a Multidimensional Hyperbolic Differential--Difference Equation with Shifts of Various Directions in the Potentials
%J Matematičeskie zametki
%D 2022
%P 810-819
%V 112
%N 6
%I mathdoc
%U http://geodesic.mathdoc.fr/item/MZM_2022_112_6_a1/
%G ru
%F MZM_2022_112_6_a1
N. V. Zaitseva. Classical Solutions of a Multidimensional Hyperbolic Differential--Difference Equation with Shifts of Various Directions in the Potentials. Matematičeskie zametki, Tome 112 (2022) no. 6, pp. 810-819. http://geodesic.mathdoc.fr/item/MZM_2022_112_6_a1/