BLOW UP OF SOLUTIONS TO THE SECOND SOUND EQUATION IN ONE SPACE DIMENSION

被引：9

作者：

Kato, Keiichi ^{[1
]}

Sugiyama, Yuusuke ^{[1
]}

机构：

[1] Tokyo Univ Sci, Dept Math, Shinjuku Ku, Tokyo 1628601, Japan

来源：

KYUSHU JOURNAL OF MATHEMATICS | 2013年 / 67卷 / 01期

关键词：

blow up; quasilinear hyperbolic; RAREFACTIVE SOLUTIONS; C-INFINITY; SINGULARITIES;

D O I：

10.2206/kyushujm.67.129

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

In this paper, we study blow ups of solutions to the second sound equation partial derivative(2)(t)u = u partial derivative(x)(u partial derivative(x)u), which is more natural than the second sound equation in Landau-Lifshitz's text in large time. We assume that the initial data satisfies u (0, x) >= delta > 0 for some delta. We give sufficient conditions that two types of blow up occur: one of the two types is that L-infinity-norm of partial derivative(t)u or partial derivative(x)u goes up to the infinity; the other type is that u vanishes, that is, the equation degenerates.

引用

页码：129 / 142

页数：14

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