SOLUTION BLOWUP FOR NONLINEAR EQUATIONS OF THE KHOKHLOV-ZABOLOTSKAYA TYPE

被引：15

作者：

Korpusov, M. O. ^{[1
]}

机构：

[1] Lomonosov Moscow State Univ, Moscow, Russia

来源：

THEORETICAL AND MATHEMATICAL PHYSICS | 2018年 / 194卷 / 03期

基金：

俄罗斯基础研究基金会;

关键词：

finite-time blowup; nonlinear wave; instantaneous blowup;

D O I：

10.1134/S0040577918030030

中图分类号：

O4 [物理学];

学科分类号：

0702 ;

摘要：

We consider several nonlinear evolution equations sharing a nonlinearity of the form partial derivative(2)u(2)/partial derivative t(2). Such a nonlinearity is present in the Khokhlov-Zabolotskaya equation, in other equations in the theory of nonlinear waves in a fluid, and also in equations in the theory of electromagnetic waves and ion-sound waves in a plasma. We consider sufficient conditions for a blowup regime to arise and find initial functions for which a solution understood in the classical sense is totally absent, even locally in time, i.e., we study the problem of an instantaneous blowup of classical solutions.

引用

页码：347 / 359

页数：13

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