Classical solution of the mixed problem for a nonlinear equation
https://doi.org/10.29235/1561-8323-2022-66-1-7-11
Abstract
The first mixed problem for a nonlinear equation is considered in the quarter plane. The Cauchy conditions are set at the bottom of the boundary. The Dirichlet condition is set on the left part of the boundary. The solution is constructed using the method of characteristics in an implicit analytical form as a solution of the integral equation. The solvability of these integral equations, the smoothness of the solutions, and their dependence on the initial data are investigated. The uniqueness is proved and the conditions are established, under which there exists a piecewise smooth and classical solution of the first mixed problem.
About the Authors
V. I. Korzyuk
Institute of Mathematics, National Academy of Sciences of Belarus
Belarus
Belarus
Korzyuk Viktor I. – Academician, D. Sc. (Physics and Mathematics), Professor.
11, Surganov Str., 220072, Minsk
J. V. Rudzko
Belarusian State University
Belarus
Belarus
Rudzko Jan V. – Master’s degree student.
4, Nezavisimosti Ave., 220030, Minsk
References
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2. Evans L. C. Partial differential equations. Providence, R. I., 2010. 749 p. https://doi.org/10.1090/gsm/019
3. Staliarchuk I. I. Classical solutions of the problems for Klein–Gordon–Fock equation. Hrodna, 2020. 124 p. (in Russian).
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