Existence and nonexistence of global solutions of the initial-boundary value problem for some degenerate hyperbolic equation

被引：2

作者：

Ye, YJ ^{[1
]}

机构：

[1] Henan Agr Univ, Dept Informat & Computat Sci, Zhengzhou 450002, Peoples R China

[2] China Acad Engn Phys, Grad Sch, Beijing 100088, Peoples R China

来源：

ACTA MATHEMATICA SCIENTIA | 2005年 / 25卷 / 04期

关键词：

degenerate hyperbolic equations; global existence and global nonexistence; initial-boundary value problem;

D O I：

10.1016/S0252-9602(17)30210-2

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

The author considers the global existence and global nonexistence of the initial-boundary value problem for some degenerate hyperbolic equation of the form u(tt) - div (vertical bar del u vertical bar(p-2) del u) = vertical bar u vertical bar(m)u, (x, t) is an element of (0, + infinity) x Omega with p > 2 and m > 0. He deals with the global solutions by D.H. Sattinger's potential well ideas. At the same time, when the initial energy is positive, but appropriately bounded, the global nonexistence of solutions is verified by using the analysis method.

引用

页码：703 / 709

页数：7

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