Classical Solutions of a Multidimensional Hyperbolic Differential-Difference Equation with Shifts of Various Directions in the Potentials

被引：7
作者：
Zaitseva, N. V. [1 ,2 ]
机构：
[1] Lomonosov Moscow State Univ, Moscow 119991, Russia
[2] Moscow Ctr Fundamental & Appl Math, Moscow 119991, Russia
来源：
MATHEMATICAL NOTES | 2022年 / 112卷 / 5-6期
关键词：
hyperbolic equation; differential-difference equation; classical solution; operational scheme; Fourier transform;
D O I：
10.1134/S0001434622110219
中图分类号：
O1 [数学];
学科分类号：
0701 ; 070101 ;
摘要：
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.
引用
收藏
页码：872 / 880
页数：9
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