CLASSICAL SOLUTION OF THE MIXED PROBLEM FOR A NONLINEAR EQUATION

被引：0

作者：

Korzyuk, Viktor I. ^{[1
]}

V. Rudzko, Jan ^{[2
]}

机构：

[1] Natl Acad Sci Belarus, Inst Math, 11 Surganov Str, Minsk 220072, BELARUS

[2] Belarusian State Univ, 4 Nezavisimosti Ave, Minsk 220030, BELARUS

来源：

DOKLADY NATSIONALNOI AKADEMII NAUK BELARUSI | 2022年 / 66卷 / 01期

关键词：

nonlinear equation; classical solution; mixed problem; method of characteristics;

D O I：

10.29235/1561-8323-2022-66-1-7-11

中图分类号：

O [数理科学和化学]; P [天文学、地球科学]; Q [生物科学]; N [自然科学总论];

学科分类号：

07 ; 0710 ; 09 ;

摘要：

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.

引用

页码：7 / 11

页数：5

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