Classical solution of the first mixed problem for the wave equation in the cylyndrical domain
https://doi.org/10.29235/1561-8323-2021-65-2-135-138
Abstract
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.
About the Authors
V. I. Korzyuk
Institute of Mathematics of the National Academy of Sciences of Belarus
Belarus
Belarus
Korzyuk Viktor I., Academician, D. Sc. (Physics and Mathematics), Professor
11, Surganov Str., 220072, Minsk
I. I. Stolyarchuk
Belarusian State University
Belarus
Belarus
Korzyuk Viktor I., Academician, D. Sc. (Physics and Mathematics), Professor
11, Surganov Str., 220072, Minsk
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