﻿ 多重非线性退化的p-Laplacian抛物方程组解的爆破 Blowup of Solutions for a System of Doubly Nonlinear Degenerate Parabolic Equations with p-Laplacian

Vol.04 No.02(2015), Article ID:15213,6 pages
10.12677/AAM.2015.42018

Blowup of Solutions for a System of Doubly Nonlinear Degenerate Parabolic Equations with p-Laplacian

Longfei Qi, Jing Su, Qingying Hu

College of Science, Henan University of Technology, Zhengzhou Henan

Email: slxhqy@163.com

Received: Apr. 24th, 2015; accepted: May 7th, 2015; published: May 13th, 2015

ABSTRACT

This paper is concerned with a system of doubly nonlinear degenerate parabolic equations with p-Laplacian. We prove that, under suitable conditions on the nonlinearity and certain initial datum, the lower bound for the blowup time is given if blowup does occur by using a modification of Levine’s concavity method.

Keywords:Blowup of Solution, Doubly Nonlinear Parabolic Equations, Levine’s Concavity Method

Email: slxhqy@163.com

1. 引言

(1.1)

(1.2)

(1.3)

(1.4)

(1.5)

Korpusov和Sveshnikov [22] [23] 及Polat [24] 则对如下方程的初边值问题

2. 假设和引理

(A1)，存在函数使得

,

，即

3. 主要结果及证明

(3.1)

(3.2)

(3.3)

(3.4)

(3.5)

(3.6)

(3.7)

(3.8)

(3.9)

(3.10)

(3.11)

(3.11)关于t积分得

(3.12)

(3.13)

(3.10)结合(3.13)，并用到

， (3.14)

(3.15)

(3.16)

Blowup of Solutions for a System of Doubly Nonlinear Degenerate Parabolic Equations with p-Laplacian. 应用数学进展,02,129-135. doi: 10.12677/AAM.2015.42018

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