Solution of the wave equation in a quarter plane

V. I. Korzyuk^ab, I. S. Kozlovskaja^ab, V. Yu. Sokolovich<sup>ab

a</sup> Belarusian State University, Minsk
^b Institute of Mathematics of the National Academy of Sciences of Belarus, Minsk

Abstract: In this article, the classical solution in the class of continuously differentiable functions of arbitrary order in the quarter plane for the wave equation is presented in an analytical form. The classical solution of the equation under consideration is determined. To construct this solution, a partial solution of the original wave equation is written out. For the given functions, the obtained matching conditions are necessary and sufficient for the presented solution of the equation to be classical of high order of smoothness.

UDC: 517.958

Received: 01.06.2020