To the Problem of Discontinuous Solutions in Applied Mathematics

被引:0
|
作者
Vasiliev, Valery V. V. [1 ]
Lurie, Sergey A. A. [1 ]
机构
[1] Russian Acad Sci, Inst Appl Mech, Moscow 125040, Russia
基金
俄罗斯科学基金会;
关键词
differential calculus; applied mathematics; equations of mathematical physics; discontinuous and singular solutions;
D O I
10.3390/math11153362
中图分类号
O1 [数学];
学科分类号
0701 ; 070101 ;
摘要
This paper addresses discontinuities in the solutions of mathematical physics that describe actual processes and are not observed in experiments. The appearance of discontinuities is associated in this paper with the classical differential calculus based on the analysis of infinitesimal quantities. Nonlocal functions and nonlocal derivatives, which are not specified, in contrast to the traditional approach to a point, but are the results of averaging over small but finite intervals of the independent variable are introduced. Classical equations of mathematical physics preserve the traditional form but include nonlocal functions. These equations are supplemented with additional equations that link nonlocal and traditional functions. The proposed approach results in continuous solutions of the classical singular problems of mathematical physics. The problems of a string and a circular membrane loaded with concentrated forces are used to demonstrate the procedure. Analytical results are supported with experimental data.
引用
收藏
页数:10
相关论文
共 50 条