Applied Mathematics and Mechanics

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

Blow-Up Estimates for a Non-Newtonian Filtration System

  • Zuo-dong Yang
  • Qi-shao Lu


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.

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


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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.Google Scholar
  2. [2]
    Mitidieri E. Nonexistence of positive solutions of semi-linear elliptic system in R N[J]. Differential Integral Equations,1996,9(3):465–479.Google 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.Google 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.Google 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.Google 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.Google 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.Google 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. An L blow-up estimate for a nonlinear heat equation[J]. Comm Pure Appl Math,1985, 38(3):291–295.Google 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.Google Scholar
  12. [12]
    YANG Zuo-dong. Non-existence of positive entire solutions for elliptic inequalities of p-Laplacian[J]. Appl Math J Chinese Univ,1997,12B(4):399–410.Google Scholar

Copyright information

© Kluwer Academic Publishers 2001

Authors and Affiliations

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

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