Method of reflections for the Klein–Gordon equation
https://doi.org/10.29235/1561-8323-2022-66-3-263-268
Abstract
Using the method of reflections, the solutions of the first and second mixed problem for the homogenous Klein–Gordon equation in a quarter plane and of the first mixed problem for the homogenous Klein–Gordon equation in a halfstrip are written out in an explicit analytical form. The Cauchy conditions of these problems are inhomogeneous, but the Dirichlet boundary condition (or the Neumann boundary condition) is homogeneous. Conditions are formulated, under which the solutions to these problems are classical.
About the Authors
V. I. Korzyuk
Institute of Mathematics of the National Academy of Sciences of Belarus; Belarusian State University
Belarus
Belarus
Korzyuk Viktor I. – Academician, D. Sc. (Physics and Ma thematics), Professor
11, Surganov Str., 220072, Minsk
J. V. Rudzko
Belarusian State University
Belarus
Belarus
Rudzko Jan V. – M. Sc. (Mathematiсs and Computer Sciences)
4, Nezavisimosti Ave., 220030, Minsk
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