CLASSICAL SOLUTION of THE FIRST MIXED PROBLEM FOR THE WAVE EQUATION IN THE CYLYNDRICAL DOMAIN

被引：0

作者：

Korzyuk, Viktor, I ^{[1
]}

Stolyarchuk, Ivan I. ^{[2
]}

机构：

[1] Natl Acad Sci Belarus, Inst Math, 11 Surganov Str, Minsk 220072, BELARUS

[2] Belarusian State Univ, Phys & Math, 4 Nezavisimosti Ave, Minsk 220030, BELARUS

来源：

DOKLADY NATSIONALNOI AKADEMII NAUK BELARUSI | 2021年 / 65卷 / 02期

关键词：

wave equation; characteristics method; sphere averaging operator; classical solution; mixed problem; matching conditions;

D O I：

10.29235/1561-8323-2021-65-2-135-138

中图分类号：

O [数理科学和化学]; P [天文学、地球科学]; Q [生物科学]; N [自然科学总论];

学科分类号：

07 ; 0710 ; 09 ;

摘要：

The first mixed problem for the wave equation in the four-dimensional area (three dimensions of space and one dimension of time) is considered. The theorem of existence of the unique classical solution of the given problem is proved with the help of averaging operators. The method of averaging operators was used for obtaining Kirchhoff's and Poisson's formulas for solving the Cauchy problem for the wave equation in the case of four and three independent variables respectively. Here it is shown that this approach can be used to solve a more complex problem. When using averaging operators, the initial problem is reduced to the first mixed problem for string oscillations, for which the correct solvability criterion has already been proved. However, the smoothness of the functions in the solvability criterion should be enhanced. The enhanced criterion can be proved by the method of characteristics.

引用

页码：135 / 138

页数：4

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