一类非牛顿渗流系统爆破界的估计

杨作东; 陆启韶

一类非牛顿渗流系统爆破界的估计

北京航空航天大学理学院, 北京 100083

基金项目: 国家自然科学基金资助项目(19872010);教育部博士学科点基金资助项目(98000619)

详细信息

作者简介:
杨作东(1961- ),男,河北三河人,博士.

中图分类号: O175.25
计量
- 文章访问数: 2857
- HTML全文浏览量: 240
- PDF下载量: 763
- 被引次数: 0
出版历程
- 收稿日期: 2000-04-14
- 修回日期: 2000-11-29
- 刊出日期: 2001-03-15

Blow-up Estimates for a Non-Newtonian Filtration System

College of Science Beijing University of Aeronautics and Astronantics, Beijing 100083, P R China

摘要

摘要: 首先得到一类拟线性椭圆型方程组的正解的先验界估计和衰减性质,从而推出该方程组的径向非增正对称解的不存在性结果.利用此结果建立了一类拟线性反应扩散方程组(非牛顿渗流系统)的爆破界的估计,推广了半线性(Fujita型)反应扩散方程组的结果.
- 爆破 /
- 爆破速率 /
- 拟线性方程组
Abstract: The prior estimate and decay property of positive solutions are derived for a system of quasilinear elliptic differential equations first.Hence,the result of nonexistence for differential equation system of radially nonincreasing positive solutions was implied.By using this nonexistence result,blow-up estimates for a class quasilinear reaction-diffusion systems(non-Newtonian filtration systems) are established,which extencds the result of semilinear reaction-diffusion(Fujita type) systems.
- blow-up /
- blow-up rates /
- quasilinear equation system

HTML全文

参考文献(12)

[1]	Gabriella C,Mitidieri E.Blow-up estimates of positive solutions of a parabolic system[J].J Differential Equations,1994,113(2):265-271.
[2]	Mitidieri E.Nonexistence of positive solutions of semilinear elliptic system in RN[J].Diff Integral Equations,1996,9(3):465-479.
[3]	Escobedo M,Levine A H.Critical blow-up and global existence numbers for a weakly coupled system of reaction-diffusion equations[J].Arch Rational Mech Anal,1995,129(1):47-100.
[4]	Escobedo M,Herrero M M.Boundedness and blow up for a semilinear reaction-diffusion system[J].J Differential Equations,1991,89(1):176-202.
[5]	WU Z Q,Yuan H J.Uniqueness of generalized solutions for a quasilinear degenerate parabolic system[J].J Partial Differential Equations,1995,8(1):89-96.
[6]	Mitidieri E,Sweers G,Vander Vorst R.Nonexistence theorems for systems of quasilinear partial differential equations[J].Differential Integral Equations,1995,8(6):1331-1354.
[7]	Clement PH,Manasevich R,Mitidieri E.Positive solutions for a quasilinear system via blow up[J].Comm in Partial Differential Equations,1993,,18(12):2071-2106.
[8]	GUO Zong-ming.Existence of positive radial solutions for certain quasilinear elliptic systems[J].Chinese Ann Math,1996,,17A(3):573-582.
[9]	Weissler.An L^∞ blow-up estimate for a nonlinear heat equation[J].Comm Pure Appl Math,1985,38(3):291-295.
[10]	GUO Zong-ming,YANG Zuo-dong.Some uniqueness results for a class of quasilinear elliptic eigenvalue problems[J].Acta Math Sinica(new series),1998,14(2):245-260.
[11]	YANG Zuo-dong,GUO Zong-ming.On the structure of positive solutions for quasilinear ordinary differential equations[J].Appl Anal,1995,58(1):31-51.
[12]	YANG Zuo-dong.Non-Existence of positive entire solutions for elliptic inequalities of p-Laplacian[J].Appl Math J C U,1997,12B(4):399-410.