﻿ 一类非线性退化双曲方程解的整体存在性和爆破的条件 The Global Existence and Blow-Up Conditions for a Class of Nonlinear Degenerate Hyperbolic Equation

Vol.06 No.04(2017), Article ID:21436,6 pages
10.12677/AAM.2017.64063

The Global Existence and Blow-Up Conditions for a Class of Nonlinear Degenerate Hyperbolic Equation

Jialing Zhu

College of Mathematics, Southwest Jiaotong University, Chengdu Sichuan

Received: Jul. 1st, 2017; accepted: Jul. 17th, 2017; published: Jul. 20th, 2017

ABSTRACT

In this paper, the initial-boundary value problem for a class of degenerate hyperbolic equation is studied. The global existence of solution is obtained by introducing Galerkin method. Also the global nonexistence of solution can be verified by using the analysis method while the initial energy is positive and bounded.

Keywords:Degenerate Hyperbolic Equation, Galerkin Method, Global Solutions, Blow Up

1. 引言

(1.1)

(1.2)

(1.3)

Ye [3] 采采用了Galerkin方法证明了解的整体存在性，并通过分析的方法得到了解爆破的条件. 本文是问题(1.3)的一个简化模型。

2. 势井深度

，定义如下能量泛函：

(2.1)

(2.2)

3. 解整体存在和爆破的条件

(3.1)

(3.2)

(3.3)

(3.4)

(3.5)

(3.6)

(3.7)

(3.8)

(3.9)

(3.10)

，得。当时，有

The Global Existence and Blow-Up Conditions for a Class of Nonlinear Degenerate Hyperbolic Equation[J]. 应用数学进展, 2017, 06(04): 523-528. http://dx.doi.org/10.12677/AAM.2017.64063

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