Blow-up Estimates for a Non-Newtonian Filtration System

YANG Zuo-dong; LU Qi-shao

Article Contents

Article Navigation > Applied Mathematics and Mechanics > 2001 > 22(3): 287-294

YANG Zuo-dong, LU Qi-shao. Blow-up Estimates for a Non-Newtonian Filtration System[J]. Applied Mathematics and Mechanics, 2001, 22(3): 287-294.

Citation:

YANG Zuo-dong, LU Qi-shao. Blow-up Estimates for a Non-Newtonian Filtration System[J]. Applied Mathematics and Mechanics, 2001, 22(3): 287-294.

Citation:

YANG Zuo-dong, LU Qi-shao. Blow-up Estimates for a Non-Newtonian Filtration System[J]. Applied Mathematics and Mechanics, 2001, 22(3): 287-294.

PDF( 310 KB)

Blow-up Estimates for a Non-Newtonian Filtration System

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

Received Date: 2000-04-14
Rev Recd Date: 2000-11-29
Publish Date: 2001-03-15

Abstract

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

FullText(HTML)

References(12)

References

[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.