On exact solutions of a Sobolev equation

被引：4
|
作者：
Aristov, A. I. [1 ]
机构：
[1] Lomonosov Moscow State Univ, Moscow, Russia
来源：
MATHEMATICAL NOTES | 2017年 / 101卷 / 5-6期
关键词：
Sobolev space; nonlinear differential equation; algebraic and differential nonlinearities; blow-up of a solution;
D O I：
10.1134/S0001434617050194
中图分类号：
O1 [数学];
学科分类号：
0701 ; 070101 ;
摘要：
A nonlinear Sobolev-type equation that can be used to describe nonstationary processes in the semiconductor medium is studied. A number of families of exact solutions of this equation that can be expressed in terms of elementary functions and quadratures is obtained; some of these families contain arbitrary sufficiently smooth functions of one argument. The qualitative behavior of the resulting solutions is analyzed.
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页码：928 / 941
页数：14
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