Goursat’s problem on the plane for a quasilinear hyperbolic equation
https://doi.org/10.29235/1561-8323-2022-66-4-391-396
Abstract
A classical solution of the problem for a quasilinear hyperbolic equation in the case of two independent variables with given conditions for the desired function on the characteristic lines is obtained. The problem is reduced to a system of equations with a completely continuous operator. We constructed the unique solution by the method of successive approximations and showed the necessary and sufficient smoothness and matching conditions on given functions.
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
O. A. Kovnatskaya
Belarusian State University
Belarus
Belarus
Kovnatskaya Olga A. – Ph. D. (Physics and Mathematics).
4, Nezavisimosti Ave., 220030, Minsk
V. A. Sevastyuk
Institute of Mathematics of the National Academy of Sciences of Belarus
Belarus
Belarus
Sevastyuk Vladimir A. – Lead Software Developer.
11, Surganov Str., 220072, Minsk
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