Applied Mathematics and Mechanics

, Volume 22, Issue 3, pp 332–339 | Cite as

Blow-up estimates for a non-newtonian filtration system

  • Yang Zuo-dong
  • Lu Qi-shao


The prior estimate and decay property of positive solutions are derived for a system of quasi-linear elliptic differential equations first. Hence, the result of non-existence for differential equation system of radially nonincreasing positive solutions is implied. By using this non-existence result, blow-up estimates for a class quasi-linear reaction-diffusion systems (non-Newtonian filtration systems) are established, which extends the result of semi-linear reaction-diffusion (Fujita type) systems.

Key words

blow-up blow-up rates quasi-linear equation system 

CLC number



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  1. [1]
    Gabriella C, Mitidieri E. Blow-up estimates of positive solutions of a parabolic system[J].J Differential Equations, 1994,113(2):265–271.MathSciNetCrossRefGoogle Scholar
  2. [2]
    Mitidieri E. Nonexistence of positive solutions of semi-linear elliptic system inR N[J].Differential Integral Equations, 1996,9(3):465–479.zbMATHMathSciNetGoogle Scholar
  3. [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.zbMATHMathSciNetCrossRefGoogle Scholar
  4. [4]
    Escobedo M, Herrero M M. Boundedness and blow up for a semi-linear reaction-diffusion system [J].J Differential Equations, 1991,89(1):176–202.zbMATHMathSciNetCrossRefGoogle Scholar
  5. [5]
    WU Z Q, Yuan H J. Uniqueness of generalized solutions for a quasi-linear degenerate parabolic system[J].J Partial Differential Equations, 1995,8(1):89–96.zbMATHMathSciNetGoogle Scholar
  6. [6]
    Mitidieri E, Sweers G, Vorst Vander R. Nonexistence theorems for systems of quasi-linear partial differential equations[J].Differential Integral Equations, 1995,8(6):1331–1354.zbMATHMathSciNetGoogle Scholar
  7. [7]
    Clement Ph, Manasevich R, Mitidieri E. Positive solutions for a quasi-linear system via blow up [J].Comm in Partial Differential Equations, 1993,18(12):2071–2106.zbMATHMathSciNetGoogle Scholar
  8. [8]
    GUO Zong-ming. Existence of positive radial solutions for certain quasi-linear elliptic systems[J].Chinese Ann Math, 1996,17A(3):573–582.Google Scholar
  9. [9]
    Weissler. AnL blow-up estimate for a nonlinear heat equation[J].Comm Pure Appl Math, 1985,38(3):291–295.zbMATHMathSciNetGoogle Scholar
  10. [10]
    GUO Zong-ming, YANG Zuo-dong. Some uniqueness results for a class of quasi-linear elliptic eigenvalue problems[J].Acta Math Sinica (New Series), 1998,14(2):245–260.Google Scholar
  11. [11]
    YANG Zuo-dong, GUO Zong-ming. On the structure of positive solutions for quasi-linear ordinary differential equations[J].Appl Anal, 1995,58(1):31–51.MathSciNetGoogle Scholar
  12. [12]
    YANG Zuo-dong. Non-existence of positive entire solutions for elliptic inequalities ofp-Laplacian [J].Appl Math J Chinese Univ, 1997,12B(4):399–410.Google Scholar

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© Editorial Committee of Applied Mathematics and Mechanics 1980

Authors and Affiliations

  • Yang Zuo-dong
    • 1
  • Lu Qi-shao
    • 1
  1. 1.College of ScienceBeijing University of Aeronautics and AstronauticsBeijingP R China

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