Mixed problem for a one-dimensional wave equation with conjugation conditions and second-order derivatives in boundary conditions
https://doi.org/10.29235/1561-2430-2020-56-3-287-297
Abstract
In this paper, we consider the boundary problem for the half-strip on the plane for the case of two independent variables. This mixed problem is solved for a one-dimensional wave equation with Cauchy conditions on the basis of the half-strip and boundary conditions for lateral parts of the area border containing second-order derivatives. Moreover, the conjugation conditions are specified for the required function and its derivatives for the case when the homogeneous matching conditions are not satisfied. A classical solution to this problem is found in an analytical form by the characteristics method. This solution is approved to be unique if the relevant conditions are fulfilled.
About the Authors
V. I. Korzyuk
Institute of Mathematics of the National Academy of Sciences of Belarus;
Belarusian State University
Belarus
Belarus
Viktor I. Korzyuk – Academician, Professor, Dr. Sc. (Physics and Mathematics)
11, Surganov Str., 220072, Minsk
4, Nezavisimosti Ave., 220030, Minsk
S. N. Naumavets
Brest State Technical University
Belarus
Belarus
Sviatlana N. Naumavets – Senior Lecturer
267, Moskovskaya Str., 224017, Brest
V. P. Serikov
Institute of Mathematics of the National Academy of Sciences of Belarus
Belarus
Belarus
Vladimir P. Serikov – Lead Software Engineer
11, Surganov Str., 220072, Minsk
References
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