CLASSICAL SOLUTION OF THE INITIAL-VALUE PROBLEM FOR A ONE-DIMENSIONAL QUASILINEAR WAVE EQUATION

被引：6

作者：

Korzyuk, Academician Viktor I. ^{[1
]}

Rudzko, Jan, V ^{[1
]}

机构：

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

来源：

DOKLADY NATSIONALNOI AKADEMII NAUK BELARUSI | 2023年 / 67卷 / 01期

关键词：

  nonlinear wave equation; Cauchy problem; method of characteristics; fixed-point principle; classical solution; 1ST MIXED PROBLEM;

D O I：

10.29235/1561-8323-2023-67-1-14-19

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：

For a one-dimensional mildly quasilinear wave equation given in the upper half-plane, we consider the Cauchy problem. The solution is constructed by the method of characteristics in an implicit analytical form as a solution of some inte-gro-differential equation. The solvability of this equation, as well the smoothness of its solution, is studied. For the problem in question, the uniqueness of the solution is proved and the conditions under which its classical solution exists are established. When given data is not enough smooth a mild solution is constructed.

引用

页码：14 / 19

页数：6

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